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QOJ
| ID | 题目 | 提交者 | 结果 | 用时 | 内存 | 语言 | 文件大小 | 提交时间 | 测评时间 |
|---|---|---|---|---|---|---|---|---|---|
| #110344 | #6513. Expression 3 | ffao | Compile Error | / | / | C++17 | 83.7kb | 2023-06-01 16:44:06 | 2023-06-01 17:00:46 |
Judging History
你现在查看的是最新测评结果
- [2024-02-14 13:23:19]
- hack成功，自动添加数据
- (/hack/531)
- [2023-08-10 23:21:45]
- System Update: QOJ starts to keep a history of the judgings of all the submissions.
- [2023-06-01 17:00:46]
- 评测
- 测评结果：Compile Error
- 用时：0ms
- 内存：0kb
- [2023-06-01 16:44:06]
- 提交
answer
#ifdef LOCAL
#define _GLIBCXX_DEBUG 1
#define dbg(...) cerr << "LINE(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
#else
#define dbg(...) 0
#endif
#if 0
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
template<class T>
using ordered_set = __gnu_pbds::tree<T, __gnu_pbds::null_type, std::less<T>, __gnu_pbds::rb_tree_tag,
__gnu_pbds::tree_order_statistics_node_update>;
#endif
#include <vector>
#include <list>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <bitset>
#include <algorithm>
#include <numeric>
#include <utility>
#include <sstream>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <ctime>
#include <cstring>
#include <random>
#include <chrono>
#include <cassert>
using namespace std;
#define sz(x) (int)(x).size()
#define all(x) begin(x), end(x)
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define REP(i,n) for(int (i)=0;(i)<(int)(n);(i)++)
#define each(a,x) for (auto& a: x)
#define tcT template<class T
#define tcTU tcT, class U
#define tcTUU tcT, class ...U
template<class T> using V = vector<T>;
template<class T, size_t SZ> using AR = array<T,SZ>;
typedef string str;
typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<vi> vvi;
template<typename T, typename U> T &ctmax(T &x, const U &y){ return x = max<T>(x, y); }
template<typename T, typename U> T &ctmin(T &x, const U &y){ return x = min<T>(x, y); }
mt19937 rng((unsigned)chrono::steady_clock::now().time_since_epoch().count());
#define ts to_string
str ts(char c) { return str(1,c); }
str ts(bool b) { return b ? "true" : "false"; }
str ts(const char* s) { return (str)s; }
str ts(str s) { return s; }
str ts(vector<bool> v) { str res = "{"; F0R(i,sz(v)) res += char('0'+v[i]); res += "}"; return res; }
template<size_t SZ> str ts(bitset<SZ> b) { str res = ""; F0R(i,SZ) res += char('0'+b[i]); return res; }
template<class A, class B> str ts(pair<A,B> p);
template<class T> str ts(T v) { bool fst = 1; str res = "{"; for (const auto& x: v) {if (!fst) res += ", "; fst = 0; res += ts(x);} res += "}"; return res;}
template<class A, class B> str ts(pair<A,B> p) {return "("+ts(p.first)+", "+ts(p.second)+")"; }
template<class A> void pr(A x) { cout << ts(x); }
template<class H, class... T> void pr(const H& h, const T&... t) { pr(h); pr(t...); }
void ps() { pr("\n"); }
template<class H, class... T> void ps(const H& h, const T&... t) { pr(h); if (sizeof...(t)) pr(" "); ps(t...); }
void DBG() { cerr << "]" << endl; }
template<class H, class... T> void DBG(H h, T... t) {cerr << ts(h); if (sizeof...(t)) cerr << ", "; DBG(t...); }
tcTU> void re(pair<T,U>& p);
tcT> void re(V<T>& v);
tcT, size_t SZ> void re(AR<T,SZ>& a);
tcT> void re(T& x) { cin >> x; }
void re(double& d) { str t; re(t); d = stod(t); }
void re(long double& d) { str t; re(t); d = stold(t); }
tcTUU> void re(T& t, U&... u) { re(t); re(u...); }
tcTU> void re(pair<T,U>& p) { re(p.first,p.second); }
tcT> void re(V<T>& x) { each(a,x) re(a); }
tcT, size_t SZ> void re(AR<T,SZ>& x) { each(a,x) re(a); }
tcT> void rv(int n, V<T>& x) { x.rsz(n); re(x); }
constexpr bool multitest() {return 0;}
void solve();
int main() {
ios_base::sync_with_stdio(false); cin.tie(NULL);
int t = 1;
if (multitest()) cin >> t;
for (; t; t--) solve();
}
#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)
#define gnr(i,a,b) for(int i=int(b)-1;i>=int(a);i--)
tcT> using vc = vector<T>;
tcT> using vvc=vc<vc<T>>;
using uint=unsigned;
using ull=unsigned long long;
#define si(x) int(x.size())
#define per(i,b) gnr(i,0,b)
#define pb push_back
#define eb emplace_back
#define a first
#define b second
#define bg begin()
#define ed end()
struct modinfo{uint mod,root;};
template<modinfo const&ref>
struct modular{
static constexpr uint const &mod=ref.mod;
static modular root(){return modular(ref.root);}
uint v;
//modular(initializer_list<uint>ls):v(*ls.bg){}
modular(ll vv=0){s(vv%mod+mod);}
modular& s(uint vv){
v=vv<mod?vv:vv-mod;
return *this;
}
modular operator-()const{return modular()-*this;}
modular& operator+=(const modular&rhs){return s(v+rhs.v);}
modular&operator-=(const modular&rhs){return s(v+mod-rhs.v);}
modular&operator*=(const modular&rhs){
v=ull(v)*rhs.v%mod;
return *this;
}
modular&operator/=(const modular&rhs){return *this*=rhs.inv();}
modular operator+(const modular&rhs)const{return modular(*this)+=rhs;}
modular operator-(const modular&rhs)const{return modular(*this)-=rhs;}
modular operator*(const modular&rhs)const{return modular(*this)*=rhs;}
modular operator/(const modular&rhs)const{return modular(*this)/=rhs;}
modular pow(int n)const{
modular res(1),x(*this);
while(n){
if(n&1)res*=x;
x*=x;
n>>=1;
}
return res;
}
modular inv()const{return pow(mod-2);}
/*modular inv()const{
int x,y;
int g=extgcd(v,mod,x,y);
assert(g==1);
if(x<0)x+=mod;
return modular(x);
}*/
friend modular operator+(int x,const modular&y){
return modular(x)+y;
}
friend modular operator-(int x,const modular&y){
return modular(x)-y;
}
friend modular operator*(int x,const modular&y){
return modular(x)*y;
}
friend modular operator/(int x,const modular&y){
return modular(x)/y;
}
friend ostream& operator<<(ostream&os,const modular&m){
return os<<m.v;
}
friend istream& operator>>(istream&is,modular&m){
ll x;is>>x;
m=modular(x);
return is;
}
bool operator<(const modular&r)const{return v<r.v;}
bool operator==(const modular&r)const{return v==r.v;}
bool operator!=(const modular&r)const{return v!=r.v;}
explicit operator bool()const{
return v;
}
};
#define USE_FMT
/*
//998244353
const mint prim_root=3;
//in-place fft
//size of input must be a power of 2
void inplace_fmt(vector<mint>&f,const bool inv){
const int n=f.size();
const mint root=inv?prim_root.inv():prim_root;
vc<mint> g(n);
for(int b=n/2;b>=1;b/=2){
mint w=root.pow((mint::base-1)/(n/b)),p=1;
for(int i=0;i<n;i+=b*2){
rep(j,b){
f[i+j+b]*=p;
g[i/2+j]=f[i+j]+f[i+b+j];
g[n/2+i/2+j]=f[i+j]-f[i+b+j];
}
p*=w;
}
swap(f,g);
}
if(inv)rep(i,n)
f[i]*=inv[n];
}*/
//size of input must be a power of 2
//output of forward fmt is bit-reversed
//output elements are in the range [0,mod*4)
//input of inverse fmt should be bit-reversed
template<class mint>
void inplace_fmt(const int n,mint*const f,bool inv){
static constexpr uint mod=mint::mod;
static constexpr uint mod2=mod*2;
static const int L=30;
static mint g[L],ig[L],p2[L];
if(g[0].v==0){
rep(i,L){
mint w=-mint::root().pow(((mod-1)>>(i+2))*3);
g[i]=w;
ig[i]=w.inv();
p2[i]=mint(1<<i).inv();
}
}
if(!inv){
int b=n;
if(b>>=1){//input:[0,mod)
rep(i,b){
uint x=f[i+b].v;
f[i+b].v=f[i].v+mod-x;
f[i].v+=x;
}
}
if(b>>=1){//input:[0,mod*2)
mint p=1;
for(int i=0,k=0;i<n;i+=b*2){
rng(j,i,i+b){
uint x=(f[j+b]*p).v;
f[j+b].v=f[j].v+mod-x;
f[j].v+=x;
}
p*=g[__builtin_ctz(++k)];
}
}
while(b){
if(b>>=1){//input:[0,mod*3)
mint p=1;
for(int i=0,k=0;i<n;i+=b*2){
rng(j,i,i+b){
uint x=(f[j+b]*p).v;
f[j+b].v=f[j].v+mod-x;
f[j].v+=x;
}
p*=g[__builtin_ctz(++k)];
}
}
if(b>>=1){//input:[0,mod*4)
mint p=1;
for(int i=0,k=0;i<n;i+=b*2){
rng(j,i,i+b){
uint x=(f[j+b]*p).v;
f[j].v=(f[j].v<mod2?f[j].v:f[j].v-mod2);
f[j+b].v=f[j].v+mod-x;
f[j].v+=x;
}
p*=g[__builtin_ctz(++k)];
}
}
}
}else{
int b=1;
if(b<n/2){//input:[0,mod)
mint p=1;
for(int i=0,k=0;i<n;i+=b*2){
rng(j,i,i+b){
ull x=f[j].v+mod-f[j+b].v;
f[j].v+=f[j+b].v;
f[j+b].v=x*p.v%mod;
}
p*=ig[__builtin_ctz(++k)];
}
b<<=1;
}
for(;b<n/2;b<<=1){
mint p=1;
for(int i=0,k=0;i<n;i+=b*2){
rng(j,i,i+b/2){//input:[0,mod*2)
ull x=f[j].v+mod2-f[j+b].v;
f[j].v+=f[j+b].v;
f[j].v=(f[j].v)<mod2?f[j].v:f[j].v-mod2;
f[j+b].v=x*p.v%mod;
}
rng(j,i+b/2,i+b){//input:[0,mod)
ull x=f[j].v+mod-f[j+b].v;
f[j].v+=f[j+b].v;
f[j+b].v=x*p.v%mod;
}
p*=ig[__builtin_ctz(++k)];
}
}
if(b<n){//input:[0,mod*2)
rep(i,b){
uint x=f[i+b].v;
f[i+b].v=f[i].v+mod2-x;
f[i].v+=x;
}
}
mint z=p2[__lg(n)];
rep(i,n)f[i]*=z;
}
}
template<class mint>
void inplace_fmt(vector<mint>&f,bool inv){
inplace_fmt(si(f),f.data(),inv);
}
template<class mint>
void half_fmt(const int n,mint*const f){
static constexpr uint mod=mint::mod;
static constexpr uint mod2=mod*2;
static const int L=30;
static mint g[L],h[L];
if(g[0].v==0){
rep(i,L){
g[i]=-mint::root().pow(((mod-1)>>(i+2))*3);
h[i]=mint::root().pow((mod-1)>>(i+2));
}
}
int b=n;
int lv=0;
if(b>>=1){//input:[0,mod)
mint p=h[lv++];
for(int i=0,k=0;i<n;i+=b*2){
rng(j,i,i+b){
uint x=(f[j+b]*p).v;
f[j+b].v=f[j].v+mod-x;
f[j].v+=x;
}
p*=g[__builtin_ctz(++k)];
}
}
if(b>>=1){//input:[0,mod*2)
mint p=h[lv++];
for(int i=0,k=0;i<n;i+=b*2){
rng(j,i,i+b){
uint x=(f[j+b]*p).v;
f[j+b].v=f[j].v+mod-x;
f[j].v+=x;
}
p*=g[__builtin_ctz(++k)];
}
}
while(b){
if(b>>=1){//input:[0,mod*3)
mint p=h[lv++];
for(int i=0,k=0;i<n;i+=b*2){
rng(j,i,i+b){
uint x=(f[j+b]*p).v;
f[j+b].v=f[j].v+mod-x;
f[j].v+=x;
}
p*=g[__builtin_ctz(++k)];
}
}
if(b>>=1){//input:[0,mod*4)
mint p=h[lv++];
for(int i=0,k=0;i<n;i+=b*2){
rng(j,i,i+b){
uint x=(f[j+b]*p).v;
f[j].v=(f[j].v<mod2?f[j].v:f[j].v-mod2);
f[j+b].v=f[j].v+mod-x;
f[j].v+=x;
}
p*=g[__builtin_ctz(++k)];
}
}
}
}
template<class mint>
void half_fmt(vector<mint>&f){
half_fmt(si(f),f.data());
}
/*template<class mint>
vc<mint> multiply(vc<mint> x,const vc<mint>&y,bool same=false){
int n=si(x)+si(y)-1;
int s=1;
while(s<n)s*=2;
x.resize(s);inplace_fmt(x,false);
if(!same){
vc<mint> z(s);
rep(i,si(y))z[i]=y[i];
inplace_fmt(z,false);
rep(i,s)x[i]*=z[i];
}else{
rep(i,s)x[i]*=x[i];
}
inplace_fmt(x,true);x.resize(n);
return x;
}*/
//59501818244292734739283969-1=5.95*10^25 までの値を正しく計算
//最終的な列の大きさが 2^24 までなら動く
//最終的な列の大きさが 2^20 以下のときは，下の 3 つの素数を使ったほうが速い（は？）
//VERIFY: yosupo
namespace arbitrary_convolution{
//constexpr modinfo base0{167772161,3};//2^25 * 5 + 1
//constexpr modinfo base1{469762049,3};//2^26 * 7 + 1
//constexpr modinfo base2{754974721,11};//2^24 * 45 + 1
constexpr modinfo base0{1045430273,3};//2^20 * 997 + 1
constexpr modinfo base1{1051721729,6};//2^20 * 1003 + 1
constexpr modinfo base2{1053818881,7};//2^20 * 1005 + 1
using mint0=modular<base0>;
using mint1=modular<base1>;
using mint2=modular<base2>;
template<class t,class mint>
vc<t> sub(const vc<mint>&x,const vc<mint>&y,bool same=false){
int n=si(x)+si(y)-1;
int s=1;
while(s<n)s*=2;
vc<t> z(s);rep(i,si(x))z[i]=x[i].v;
inplace_fmt(z,false);
if(!same){
vc<t> w(s);rep(i,si(y))w[i]=y[i].v;
inplace_fmt(w,false);
rep(i,s)z[i]*=w[i];
}else{
rep(i,s)z[i]*=z[i];
}
inplace_fmt(z,true);z.resize(n);
return z;
}
template<class mint>
vc<mint> multiply(const vc<mint>&x,const vc<mint>&y,bool same=false){
auto d0=sub<mint0>(x,y,same);
auto d1=sub<mint1>(x,y,same);
auto d2=sub<mint2>(x,y,same);
int n=si(d0);
vc<mint> res(n);
static const mint1 r01=mint1(mint0::mod).inv();
static const mint2 r02=mint2(mint0::mod).inv();
static const mint2 r12=mint2(mint1::mod).inv();
static const mint2 r02r12=r02*r12;
static const mint w1=mint(mint0::mod);
static const mint w2=w1*mint(mint1::mod);
rep(i,n){
ull a=d0[i].v;
ull b=(d1[i].v+mint1::mod-a)*r01.v%mint1::mod;
ull c=((d2[i].v+mint2::mod-a)*r02r12.v+(mint2::mod-b)*r12.v)%mint2::mod;
res[i].v=(a+b*w1.v+c*w2.v)%mint::mod;
}
return res;
}
}
using arbitrary_convolution::multiply;
template<class mint>
struct Poly:public vc<mint>{
template<class...Args>
Poly(Args...args):vc<mint>(args...){}
Poly(initializer_list<mint>init):vc<mint>(all(init)){}
int size()const{
return vc<mint>::size();
}
void ups(int s){
if(size()<s)this->resize(s,0);
}
Poly low(int s)const{
return Poly(this->bg,this->bg+min(max(s,int(1)),size()));
}
Poly rev()const{
auto r=*this;
reverse(all(r));
return r;
}
mint freq(int i)const{
return i<size()?(*this)[i]:0;
}
Poly operator-()const{
Poly res=*this;
for(auto&v:res)v=-v;
return res;
}
Poly& operator+=(const Poly&r){
ups(r.size());
rep(i,r.size())
(*this)[i]+=r[i];
return *this;
}
template<class T>
Poly& operator+=(T t){
(*this)[0]+=t;
return *this;
}
Poly& operator-=(const Poly&r){
ups(r.size());
rep(i,r.size())
(*this)[i]-=r[i];
return *this;
}
template<class T>
Poly& operator-=(T t){
(*this)[0]-=t;
return *this;
}
template<class T>
Poly& operator*=(T t){
for(auto&v:*this)
v*=t;
return *this;
}
Poly& operator*=(const Poly&r){
return *this=multiply(*this,r);
}
Poly square()const{
return multiply(*this,*this,true);
}
#ifndef USE_FMT
Poly inv(int s)const{
Poly r{mint(1)/(*this)[0]};
for(int n=1;n<s;n*=2)
r=r*2-(r.square()*low(2*n)).low(2*n);
return r.low(s);
}
#else
//source: Section 4 of "Removing redundancy from high-precision Newton iteration"
// 5/3
Poly inv(int s)const{
Poly r(s);
r[0]=mint(1)/(*this)[0];
for(int n=1;n<s;n*=2){
vc<mint> f=low(2*n);
f.resize(2*n);
inplace_fmt(f,false);
vc<mint> g=r.low(2*n);
g.resize(2*n);
inplace_fmt(g,false);
rep(i,2*n)f[i]*=g[i];
inplace_fmt(f,true);
rep(i,n)f[i]=0;
inplace_fmt(f,false);
rep(i,2*n)f[i]*=g[i];
inplace_fmt(f,true);
rng(i,n,min(2*n,s))r[i]=-f[i];
}
return r;
}
#endif
template<class T>
Poly& operator/=(T t){
return *this*=mint(1)/mint(t);
}
Poly quotient(const Poly&r,const Poly&rri)const{
int m=r.size();
assert(r[m-1].v);
int n=size();
int s=n-m+1;
if(s<=0) return {0};
return (rev().low(s)*rri.low(s)).low(s).rev();
}
Poly& operator/=(const Poly&r){
return *this=quotient(r,r.rev().inv(max(size()-r.size(),int(0))+1));
}
Poly& operator%=(const Poly&r){
*this-=*this/r*r;
return *this=low(r.size()-1);
}
Poly operator+(const Poly&r)const{return Poly(*this)+=r;}
template<class T>
Poly operator+(T t)const{return Poly(*this)+=t;}
Poly operator-(const Poly&r)const{return Poly(*this)-=r;}
template<class T>
Poly operator-(T t)const{return Poly(*this)-=t;}
template<class T>
Poly operator*(T t)const{return Poly(*this)*=t;}
Poly operator*(const Poly&r)const{return Poly(*this)*=r;}
template<class T>
Poly operator/(T t)const{return Poly(*this)/=t;}
Poly operator/(const Poly&r)const{return Poly(*this)/=r;}
Poly operator%(const Poly&r)const{return Poly(*this)%=r;}
Poly dif()const{
Poly r(max(int(0),size()-1));
rep(i,r.size())
r[i]=(*this)[i+1]*(i+1);
return r;
}
Poly inte(const mint invs[])const{
Poly r(size()+1,0);
rep(i,size())
r[i+1]=(*this)[i]*invs[i+1];
return r;
}
//VERIFY: yosupo
//opencupXvcIII GP of Peterhof H
Poly log(int s,const mint invs[])const{
return (low(s).dif()*inv(s-1)).low(s-1).inte(invs);
}
//Petrozavodsk 2019w mintay1 G
//yosupo judge
Poly exp(int s)const{
return exp2(s).a;
}
//2つほしいときはコメントアウトの位置ずらす
pair<Poly,Poly> exp2(int s,const mint invs[])const{
assert((*this)[0]==mint(0));
Poly f{1},g{1};
for(int n=1;;n*=2){
if(n>=s)break;
g=g*2-(g.square()*f).low(n);
//if(n>=s)break;
Poly q=low(n).dif();
q=q+g*(f.dif()-f*q).low(2*n-1);
f=f+(f*(low(2*n)-q.inte(invs))).low(2*n);
}
return make_pair(f.low(s),g.low(s));
}
//11/6
//VERIFY: yosupo
Poly sqrt(int s)const{
assert((*this)[0]==1);
static const mint half=mint(1)/mint(2);
vc<mint> f{1},g{1},z{1};
for(int n=1;n<s;n*=2){
rep(i,n)z[i]*=z[i];
inplace_fmt(z,true);
vc<mint> delta(2*n);
rep(i,n)delta[n+i]=z[i]-freq(i)-freq(n+i);
inplace_fmt(delta,false);
vc<mint> gbuf(2*n);
rep(i,n)gbuf[i]=g[i];
inplace_fmt(gbuf,false);
rep(i,2*n)delta[i]*=gbuf[i];
inplace_fmt(delta,true);
f.resize(2*n);
rng(i,n,2*n)f[i]=-half*delta[i];
if(2*n>=s)break;
z=f;
inplace_fmt(z,false);
vc<mint> eps=gbuf;
rep(i,2*n)eps[i]*=z[i];
inplace_fmt(eps,true);
rep(i,n)eps[i]=0;
inplace_fmt(eps,false);
rep(i,2*n)eps[i]*=gbuf[i];
inplace_fmt(eps,true);
g.resize(2*n);
rng(i,n,2*n)g[i]=-eps[i];
}
f.resize(s);
return f;
}
pair<Poly,Poly> divide(const Poly&r,const Poly&rri)const{
Poly a=quotient(r,rri);
Poly b=*this-a*r;
return make_pair(a,b.low(r.size()-1));
}
//Yukicoder No.215
Poly pow_mod(int n,const Poly&r)const{
Poly rri=r.rev().inv(r.size());
Poly cur{1},x=*this%r;
while(n){
if(n%2)
cur=(cur*x).divide(r,rri).b;
x=(x*x).divide(r,rri).b;
n/=2;
}
return cur;
}
mint eval(mint x)const{
mint r=0,w=1;
for(auto v:*this){
r+=w*v;
w*=x;
}
return r;
}
};
//source: Tellegen’s Principle into Practice
template<class mint>
struct subproduct_tree{
using poly=Poly<mint>;
int raws,s;
vvc<mint> f;
poly top;
vc<mint> inner_product(const vc<mint>&a,const vc<mint>&b){
assert(si(a)==si(b));
vc<mint> c=a;
rep(i,si(a))c[i]*=b[i];
return c;
}
void doubling_fmt(vc<mint>&dst,vc<mint> a,const mint v){
int n=si(dst);
assert(si(a)==n);
a[0]-=v*2;
half_fmt(a);
dst.resize(2*n);
rep(i,n)dst[n+i]=a[i];
}
subproduct_tree(const vc<mint>&a){
raws=si(a);
s=1;while(s<si(a))s*=2;
f.resize(s*2);
rep(i,s){
mint w=i<si(a)?a[i]:0;
f[s+i]={-w+1,-w-1};
}
top={-a[0],1};
gnr(i,1,s){
f[i]=inner_product(f[i*2],f[i*2+1]);
top.resize(si(f[i]));
copy(all(f[i]),top.bg);
inplace_fmt(top,true);
if(i==1){
top.pb(1);
top[0]-=1;
}else{
doubling_fmt(f[i],top,1);
}
}
}
vc<mint> multieval(const poly&b){
vvc<mint> c(s*2);
c[1]=top.rev().inv(si(b)).rev()*b;
c[1].erase(c[1].bg,c[1].bg+si(b)-1);
c[1].resize(s);
vc<mint> tmp;
rng(i,1,s){
int len=si(c[i]);
inplace_fmt(c[i],false);
rep(k,2){
tmp.resize(len);
copy(all(f[i*2+(k^1)]),tmp.bg);
rep(j,len)tmp[j]*=c[i][j];
inplace_fmt(tmp,true);
c[i*2+k]=vc<mint>(tmp.bg+len/2,tmp.ed);
}
}
vc<mint> ans(raws);
rep(i,raws)ans[i]=c[s+i][0];
return ans;
}
};
template<class mint>
vc<mint> multieval(const Poly<mint>&f,const vc<mint>&x){
return subproduct_tree<mint>(x).multieval(f);
}
constexpr modinfo base{998244353,3};
constexpr modinfo base1{998244352,0};
using mint=modular<base>;
using mint1=modular<base1>;
#include <limits>
#include <type_traits>
#undef rng
namespace atcoder {
namespace internal {
// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
unsigned int _m;
unsigned long long im;
// @param m `1 <= m`
explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
// @return m
unsigned int umod() const { return _m; }
// @param a `0 <= a < m`
// @param b `0 <= b < m`
// @return `a * b % m`
unsigned int mul(unsigned int a, unsigned int b) const {
// [1] m = 1
// a = b = im = 0, so okay
// [2] m >= 2
// im = ceil(2^64 / m)
// -> im * m = 2^64 + r (0 <= r < m)
// let z = a*b = c*m + d (0 <= c, d < m)
// a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
// c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
// ((ab * im) >> 64) == c or c + 1
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned long long y = x * _m;
return (unsigned int)(z - y + (z < y ? _m : 0));
}
};
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
constexpr long long bases[3] = {2, 7, 61};
for (long long a : bases) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
// Contracts:
// [1] s - m0 * a = 0 (mod b)
// [2] t - m1 * a = 0 (mod b)
// [3] s * |m1| + t * |m0| <= b
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
// [3]:
// (s - t * u) * |m1| + t * |m0 - m1 * u|
// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
// = s * |m1| + t * |m0| <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
// by [3]: |m0| <= b/g
// by g != b: |m0| < b/g
if (m0 < 0) m0 += b / s;
return {s, m0};
}
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
unsigned long long floor_sum_unsigned(unsigned long long n,
unsigned long long m,
unsigned long long a,
unsigned long long b) {
unsigned long long ans = 0;
while (true) {
if (a >= m) {
ans += n * (n - 1) / 2 * (a / m);
a %= m;
}
if (b >= m) {
ans += n * (b / m);
b %= m;
}
unsigned long long y_max = a * n + b;
if (y_max < m) break;
// y_max < m * (n + 1)
// floor(y_max / m) <= n
n = (unsigned long long)(y_max / m);
b = (unsigned long long)(y_max % m);
std::swap(m, a);
}
return ans;
}
} // namespace internal
} // namespace atcoder
namespace atcoder {
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
} // namespace atcoder
namespace atcoder {
namespace internal {
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;
} // namespace internal
template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
static_modint(T v) {
_v = (unsigned int)(v % umod());
}
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = internal::inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
template <int id> struct dynamic_modint : internal::modint_base {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = internal::barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
dynamic_modint(T v) {
long long x = (long long)(v % (long long)(mod()));
if (x < 0) x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
dynamic_modint(T v) {
_v = (unsigned int)(v % mod());
}
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator*=(const mint& rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = internal::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt(998244353);
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
} // namespace internal
} // namespace atcoder
namespace atcoder {
long long pow_mod(long long x, long long n, int m) {
assert(0 <= n && 1 <= m);
if (m == 1) return 0;
internal::barrett bt((unsigned int)(m));
unsigned int r = 1, y = (unsigned int)(internal::safe_mod(x, m));
while (n) {
if (n & 1) r = bt.mul(r, y);
y = bt.mul(y, y);
n >>= 1;
}
return r;
}
long long inv_mod(long long x, long long m) {
assert(1 <= m);
auto z = internal::inv_gcd(x, m);
assert(z.first == 1);
return z.second;
}
// (rem, mod)
std::pair<long long, long long> crt(const std::vector<long long>& r,
const std::vector<long long>& m) {
assert(r.size() == m.size());
int n = int(r.size());
// Contracts: 0 <= r0 < m0
long long r0 = 0, m0 = 1;
for (int i = 0; i < n; i++) {
assert(1 <= m[i]);
long long r1 = internal::safe_mod(r[i], m[i]), m1 = m[i];
if (m0 < m1) {
std::swap(r0, r1);
std::swap(m0, m1);
}
if (m0 % m1 == 0) {
if (r0 % m1 != r1) return {0, 0};
continue;
}
// assume: m0 > m1, lcm(m0, m1) >= 2 * max(m0, m1)
// (r0, m0), (r1, m1) -> (r2, m2 = lcm(m0, m1));
// r2 % m0 = r0
// r2 % m1 = r1
// -> (r0 + x*m0) % m1 = r1
// -> x*u0*g = r1-r0 (mod u1*g) (u0*g = m0, u1*g = m1)
// -> x = (r1 - r0) / g * inv(u0) (mod u1)
// im = inv(u0) (mod u1) (0 <= im < u1)
long long g, im;
std::tie(g, im) = internal::inv_gcd(m0, m1);
long long u1 = (m1 / g);
// |r1 - r0| < (m0 + m1) <= lcm(m0, m1)
if ((r1 - r0) % g) return {0, 0};
// u1 * u1 <= m1 * m1 / g / g <= m0 * m1 / g = lcm(m0, m1)
long long x = (r1 - r0) / g % u1 * im % u1;
// |r0| + |m0 * x|
// < m0 + m0 * (u1 - 1)
// = m0 + m0 * m1 / g - m0
// = lcm(m0, m1)
r0 += x * m0;
m0 *= u1; // -> lcm(m0, m1)
if (r0 < 0) r0 += m0;
}
return {r0, m0};
}
long long floor_sum(long long n, long long m, long long a, long long b) {
assert(0 <= n && n < (1LL << 32));
assert(1 <= m && m < (1LL << 32));
unsigned long long ans = 0;
if (a < 0) {
unsigned long long a2 = internal::safe_mod(a, m);
ans -= 1ULL * n * (n - 1) / 2 * ((a2 - a) / m);
a = a2;
}
if (b < 0) {
unsigned long long b2 = internal::safe_mod(b, m);
ans -= 1ULL * n * ((b2 - b) / m);
b = b2;
}
return ans + internal::floor_sum_unsigned(n, m, a, b);
}
} // namespace atcoder
namespace suisen {
// ! utility
template <typename ...Types>
using constraints_t = std::enable_if_t<std::conjunction_v<Types...>, std::nullptr_t>;
template <bool cond_v, typename Then, typename OrElse>
constexpr decltype(auto) constexpr_if(Then&& then, OrElse&& or_else) {
if constexpr (cond_v) {
return std::forward<Then>(then);
} else {
return std::forward<OrElse>(or_else);
}
}
// ! function
template <typename ReturnType, typename Callable, typename ...Args>
using is_same_as_invoke_result = std::is_same<std::invoke_result_t<Callable, Args...>, ReturnType>;
template <typename F, typename T>
using is_uni_op = is_same_as_invoke_result<T, F, T>;
template <typename F, typename T>
using is_bin_op = is_same_as_invoke_result<T, F, T, T>;
template <typename Comparator, typename T>
using is_comparator = std::is_same<std::invoke_result_t<Comparator, T, T>, bool>;
// ! integral
template <typename T, typename = constraints_t<std::is_integral<T>>>
constexpr int bit_num = std::numeric_limits<std::make_unsigned_t<T>>::digits;
template <typename T, unsigned int n>
struct is_nbit { static constexpr bool value = bit_num<T> == n; };
template <typename T, unsigned int n>
static constexpr bool is_nbit_v = is_nbit<T, n>::value;
// ?
template <typename T>
struct safely_multipliable {};
template <>
struct safely_multipliable<int> { using type = long long; };
template <>
struct safely_multipliable<long long> { using type = __int128_t; };
template <>
struct safely_multipliable<unsigned int> { using type = unsigned long long; };
template <>
struct safely_multipliable<unsigned long int> { using type = __uint128_t; };
template <>
struct safely_multipliable<unsigned long long> { using type = __uint128_t; };
template <>
struct safely_multipliable<float> { using type = float; };
template <>
struct safely_multipliable<double> { using type = double; };
template <>
struct safely_multipliable<long double> { using type = long double; };
template <typename T>
using safely_multipliable_t = typename safely_multipliable<T>::type;
template <typename T, typename = void>
struct rec_value_type {
using type = T;
};
template <typename T>
struct rec_value_type<T, std::void_t<typename T::value_type>> {
using type = typename rec_value_type<typename T::value_type>::type;
};
template <typename T>
using rec_value_type_t = typename rec_value_type<T>::type;
} // namespace suisen
#include <cstdint>
#include <iterator>
#include <tuple>
namespace suisen {
namespace internal::montgomery {
template <typename Int, typename DInt>
struct Montgomery {
private:
static constexpr uint32_t bits = std::numeric_limits<Int>::digits;
static constexpr Int mask = ~Int(0);
// R = 2**32 or 2**64
// 1. N is an odd number
// 2. N < R
// 3. gcd(N, R) = 1
// 4. R * R2 - N * N2 = 1
// 5. 0 < R2 < N
// 6. 0 < N2 < R
Int N, N2, R2;
// RR = R * R (mod N)
Int RR;
public:
constexpr Montgomery() = default;
explicit constexpr Montgomery(Int N) : N(N), N2(calcN2(N)), R2(calcR2(N, N2)), RR(calcRR(N)) {
assert(N & 1);
}
// @returns t * R (mod N)
constexpr Int make(Int t) const {
return reduce(static_cast<DInt>(t) * RR);
}
// @returns T * R^(-1) (mod N)
constexpr Int reduce(DInt T) const {
// 0 <= T < RN
// Note:
// 1. m = T * N2 (mod R)
// 2. 0 <= m < R
DInt m = modR(static_cast<DInt>(modR(T)) * N2);
// Note:
// T + m * N = T + T * N * N2 = T + T * (R * R2 - 1) = 0 (mod R)
// => (T + m * N) / R is an integer.
// => t * R = T + m * N = T (mod N)
// => t = T R^(-1) (mod N)
DInt t = divR(T + m * N);
// Note:
// 1. 0 <= T < RN
// 2. 0 <= mN < RN (because 0 <= m < R)
// => 0 <= T + mN < 2RN
// => 0 <= t < 2N
return t >= N ? t - N : t;
}
constexpr Int add(Int A, Int B) const {
return (A += B) >= N ? A - N : A;
}
constexpr Int sub(Int A, Int B) const {
return (A -= B) < 0 ? A + N : A;
}
constexpr Int mul(Int A, Int B) const {
return reduce(static_cast<DInt>(A) * B);
}
constexpr Int div(Int A, Int B) const {
return reduce(static_cast<DInt>(A) * inv(B));
}
constexpr Int inv(Int A) const; // TODO: Implement
constexpr Int pow(Int A, long long b) const {
Int P = make(1);
for (; b; b >>= 1) {
if (b & 1) P = mul(P, A);
A = mul(A, A);
}
return P;
}
private:
static constexpr Int divR(DInt t) { return t >> bits; }
static constexpr Int modR(DInt t) { return t & mask; }
static constexpr Int calcN2(Int N) {
// - N * N2 = 1 (mod R)
// N2 = -N^{-1} (mod R)
// calculates N^{-1} (mod R) by Newton's method
DInt invN = N; // = N^{-1} (mod 2^2)
for (uint32_t cur_bits = 2; cur_bits < bits; cur_bits *= 2) {
// loop invariant: invN = N^{-1} (mod 2^cur_bits)
// x = a^{-1} mod m => x(2-ax) = a^{-1} mod m^2 because:
// ax = 1 (mod m)
// => (ax-1)^2 = 0 (mod m^2)
// => 2ax - a^2x^2 = 1 (mod m^2)
// => a(x(2-ax)) = 1 (mod m^2)
invN = modR(invN * modR(2 - N * invN));
}
assert(modR(N * invN) == 1);
return modR(-invN);
}
static constexpr Int calcR2(Int N, Int N2) {
// R * R2 - N * N2 = 1
// => R2 = (1 + N * N2) / R
return divR(1 + static_cast<DInt>(N) * N2);
}
static constexpr Int calcRR(Int N) {
return -DInt(N) % N;
}
};
} // namespace internal::montgomery
using Montgomery32 = internal::montgomery::Montgomery<uint32_t, uint64_t>;
using Montgomery64 = internal::montgomery::Montgomery<uint64_t, __uint128_t>;
} // namespace suisen
namespace suisen::miller_rabin {
namespace internal {
constexpr uint64_t THRESHOLD_1 = 341531ULL;
constexpr uint64_t BASE_1[]{ 9345883071009581737ULL };
constexpr uint64_t THRESHOLD_2 = 1050535501ULL;
constexpr uint64_t BASE_2[]{ 336781006125ULL, 9639812373923155ULL };
constexpr uint64_t THRESHOLD_3 = 350269456337ULL;
constexpr uint64_t BASE_3[]{ 4230279247111683200ULL, 14694767155120705706ULL, 16641139526367750375ULL };
constexpr uint64_t THRESHOLD_4 = 55245642489451ULL;
constexpr uint64_t BASE_4[]{ 2ULL, 141889084524735ULL, 1199124725622454117ULL, 11096072698276303650ULL };
constexpr uint64_t THRESHOLD_5 = 7999252175582851ULL;
constexpr uint64_t BASE_5[]{ 2ULL, 4130806001517ULL, 149795463772692060ULL, 186635894390467037ULL, 3967304179347715805ULL };
constexpr uint64_t THRESHOLD_6 = 585226005592931977ULL;
constexpr uint64_t BASE_6[]{ 2ULL, 123635709730000ULL, 9233062284813009ULL, 43835965440333360ULL, 761179012939631437ULL, 1263739024124850375ULL };
constexpr uint64_t BASE_7[]{ 2U, 325U, 9375U, 28178U, 450775U, 9780504U, 1795265022U };
template <auto BASE, std::size_t SIZE>
constexpr bool miller_rabin(uint64_t n) {
if (n == 2 or n == 3 or n == 5 or n == 7) return true;
if (n <= 1 or n % 2 == 0 or n % 3 == 0 or n % 5 == 0 or n % 7 == 0) return false;
if (n < 121) return true;
const uint32_t s = __builtin_ctzll(n - 1); // >= 1
const uint64_t d = (n - 1) >> s;
const Montgomery64 mg{ n };
const uint64_t one = mg.make(1), minus_one = mg.make(n - 1);
for (std::size_t i = 0; i < SIZE; ++i) {
uint64_t a = BASE[i] % n;
if (a == 0) continue;
uint64_t Y = mg.pow(mg.make(a), d);
if (Y == one) continue;
for (uint32_t r = 0;; ++r, Y = mg.mul(Y, Y)) {
// Y = a^(d 2^r)
if (Y == minus_one) break;
if (r == s - 1) return false;
}
}
return true;
}
}
template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
constexpr bool is_prime(T n) {
if constexpr (std::is_signed_v<T>) {
assert(n >= 0);
}
const std::make_unsigned_t<T> n_unsigned = n;
assert(n_unsigned <= std::numeric_limits<uint64_t>::max()); // n < 2^64
using namespace internal;
if (n_unsigned < THRESHOLD_1) return miller_rabin<BASE_1, 1>(n_unsigned);
if (n_unsigned < THRESHOLD_2) return miller_rabin<BASE_2, 2>(n_unsigned);
if (n_unsigned < THRESHOLD_3) return miller_rabin<BASE_3, 3>(n_unsigned);
if (n_unsigned < THRESHOLD_4) return miller_rabin<BASE_4, 4>(n_unsigned);
if (n_unsigned < THRESHOLD_5) return miller_rabin<BASE_5, 5>(n_unsigned);
if (n_unsigned < THRESHOLD_6) return miller_rabin<BASE_6, 6>(n_unsigned);
return miller_rabin<BASE_7, 7>(n_unsigned);
}
} // namespace suisen::miller_rabin
#include <vector>
namespace suisen::internal::sieve {
constexpr std::uint8_t K = 8;
constexpr std::uint8_t PROD = 2 * 3 * 5;
constexpr std::uint8_t RM[K] = { 1, 7, 11, 13, 17, 19, 23, 29 };
constexpr std::uint8_t DR[K] = { 6, 4, 2, 4, 2, 4, 6, 2 };
constexpr std::uint8_t DF[K][K] = {
{ 0, 0, 0, 0, 0, 0, 0, 1 }, { 1, 1, 1, 0, 1, 1, 1, 1 },
{ 2, 2, 0, 2, 0, 2, 2, 1 }, { 3, 1, 1, 2, 1, 1, 3, 1 },
{ 3, 3, 1, 2, 1, 3, 3, 1 }, { 4, 2, 2, 2, 2, 2, 4, 1 },
{ 5, 3, 1, 4, 1, 3, 5, 1 }, { 6, 4, 2, 4, 2, 4, 6, 1 },
};
constexpr std::uint8_t DRP[K] = { 48, 32, 16, 32, 16, 32, 48, 16 };
constexpr std::uint8_t DFP[K][K] = {
{ 0, 0, 0, 0, 0, 0, 0, 8 }, { 8, 8, 8, 0, 8, 8, 8, 8 },
{ 16, 16, 0, 16, 0, 16, 16, 8 }, { 24, 8, 8, 16, 8, 8, 24, 8 },
{ 24, 24, 8, 16, 8, 24, 24, 8 }, { 32, 16, 16, 16, 16, 16, 32, 8 },
{ 40, 24, 8, 32, 8, 24, 40, 8 }, { 48, 32, 16, 32, 16, 32, 48, 8 },
};
constexpr std::uint8_t MASK[K][K] = {
{ 0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80 }, { 0x02, 0x20, 0x10, 0x01, 0x80, 0x08, 0x04, 0x40 },
{ 0x04, 0x10, 0x01, 0x40, 0x02, 0x80, 0x08, 0x20 }, { 0x08, 0x01, 0x40, 0x20, 0x04, 0x02, 0x80, 0x10 },
{ 0x10, 0x80, 0x02, 0x04, 0x20, 0x40, 0x01, 0x08 }, { 0x20, 0x08, 0x80, 0x02, 0x40, 0x01, 0x10, 0x04 },
{ 0x40, 0x04, 0x08, 0x80, 0x01, 0x10, 0x20, 0x02 }, { 0x80, 0x40, 0x20, 0x10, 0x08, 0x04, 0x02, 0x01 },
};
constexpr std::uint8_t OFFSET[K][K] = {
{ 0, 1, 2, 3, 4, 5, 6, 7, },
{ 1, 5, 4, 0, 7, 3, 2, 6, },
{ 2, 4, 0, 6, 1, 7, 3, 5, },
{ 3, 0, 6, 5, 2, 1, 7, 4, },
{ 4, 7, 1, 2, 5, 6, 0, 3, },
{ 5, 3, 7, 1, 6, 0, 4, 2, },
{ 6, 2, 3, 7, 0, 4, 5, 1, },
{ 7, 6, 5, 4, 3, 2, 1, 0, },
};
constexpr std::uint8_t mask_to_index(const std::uint8_t bits) {
switch (bits) {
case 1 << 0: return 0;
case 1 << 1: return 1;
case 1 << 2: return 2;
case 1 << 3: return 3;
case 1 << 4: return 4;
case 1 << 5: return 5;
case 1 << 6: return 6;
case 1 << 7: return 7;
default: assert(false);
}
}
} // namespace suisen::internal::sieve
namespace suisen {
template <unsigned int N>
class SimpleSieve {
private:
static constexpr unsigned int siz = N / internal::sieve::PROD + 1;
static std::uint8_t flag[siz];
public:
SimpleSieve() {
using namespace internal::sieve;
flag[0] |= 1;
unsigned int k_max = (unsigned int) std::sqrt(N + 2) / PROD;
for (unsigned int kp = 0; kp <= k_max; ++kp) {
for (std::uint8_t bits = ~flag[kp]; bits; bits &= bits - 1) {
const std::uint8_t mp = mask_to_index(bits & -bits), m = RM[mp];
unsigned int kr = kp * (PROD * kp + 2 * m) + m * m / PROD;
for (std::uint8_t mq = mp; kr < siz; kr += kp * DR[mq] + DF[mp][mq], ++mq &= 7) {
flag[kr] |= MASK[mp][mq];
}
}
}
}
std::vector<int> prime_list(unsigned int max_val = N) const {
using namespace internal::sieve;
std::vector<int> res { 2, 3, 5 };
res.reserve(max_val / 25);
for (unsigned int i = 0, offset = 0; i < siz and offset < max_val; ++i, offset += PROD) {
for (uint8_t f = ~flag[i]; f;) {
uint8_t g = f & -f;
res.push_back(offset + RM[mask_to_index(g)]);
f ^= g;
}
}
while (res.size() and (unsigned int) res.back() > max_val) res.pop_back();
return res;
}
bool is_prime(const unsigned int p) const {
using namespace internal::sieve;
switch (p) {
case 2: case 3: case 5: return true;
default:
switch (p % PROD) {
case RM[0]: return ((flag[p / PROD] >> 0) & 1) == 0;
case RM[1]: return ((flag[p / PROD] >> 1) & 1) == 0;
case RM[2]: return ((flag[p / PROD] >> 2) & 1) == 0;
case RM[3]: return ((flag[p / PROD] >> 3) & 1) == 0;
case RM[4]: return ((flag[p / PROD] >> 4) & 1) == 0;
case RM[5]: return ((flag[p / PROD] >> 5) & 1) == 0;
case RM[6]: return ((flag[p / PROD] >> 6) & 1) == 0;
case RM[7]: return ((flag[p / PROD] >> 7) & 1) == 0;
default: return false;
}
}
}
};
template <unsigned int N>
std::uint8_t SimpleSieve<N>::flag[SimpleSieve<N>::siz];
template <unsigned int N>
class Sieve {
private:
static constexpr unsigned int base_max = (N + 1) * internal::sieve::K / internal::sieve::PROD;
static unsigned int pf[base_max + internal::sieve::K];
public:
Sieve() {
using namespace internal::sieve;
pf[0] = 1;
unsigned int k_max = ((unsigned int) std::sqrt(N + 1) - 1) / PROD;
for (unsigned int kp = 0; kp <= k_max; ++kp) {
const int base_i = kp * K, base_act_i = kp * PROD;
for (int mp = 0; mp < K; ++mp) {
const int m = RM[mp], i = base_i + mp;
if (pf[i] == 0) {
unsigned int act_i = base_act_i + m;
unsigned int base_k = (kp * (PROD * kp + 2 * m) + m * m / PROD) * K;
for (std::uint8_t mq = mp; base_k <= base_max; base_k += kp * DRP[mq] + DFP[mp][mq], ++mq &= 7) {
pf[base_k + OFFSET[mp][mq]] = act_i;
}
}
}
}
}
bool is_prime(const unsigned int p) const {
using namespace internal::sieve;
switch (p) {
case 2: case 3: case 5: return true;
default:
switch (p % PROD) {
case RM[0]: return pf[p / PROD * K + 0] == 0;
case RM[1]: return pf[p / PROD * K + 1] == 0;
case RM[2]: return pf[p / PROD * K + 2] == 0;
case RM[3]: return pf[p / PROD * K + 3] == 0;
case RM[4]: return pf[p / PROD * K + 4] == 0;
case RM[5]: return pf[p / PROD * K + 5] == 0;
case RM[6]: return pf[p / PROD * K + 6] == 0;
case RM[7]: return pf[p / PROD * K + 7] == 0;
default: return false;
}
}
}
int prime_factor(const unsigned int p) const {
using namespace internal::sieve;
switch (p % PROD) {
case 0: case 2: case 4: case 6: case 8:
case 10: case 12: case 14: case 16: case 18:
case 20: case 22: case 24: case 26: case 28: return 2;
case 3: case 9: case 15: case 21: case 27: return 3;
case 5: case 25: return 5;
case RM[0]: return pf[p / PROD * K + 0] ? pf[p / PROD * K + 0] : p;
case RM[1]: return pf[p / PROD * K + 1] ? pf[p / PROD * K + 1] : p;
case RM[2]: return pf[p / PROD * K + 2] ? pf[p / PROD * K + 2] : p;
case RM[3]: return pf[p / PROD * K + 3] ? pf[p / PROD * K + 3] : p;
case RM[4]: return pf[p / PROD * K + 4] ? pf[p / PROD * K + 4] : p;
case RM[5]: return pf[p / PROD * K + 5] ? pf[p / PROD * K + 5] : p;
case RM[6]: return pf[p / PROD * K + 6] ? pf[p / PROD * K + 6] : p;
case RM[7]: return pf[p / PROD * K + 7] ? pf[p / PROD * K + 7] : p;
default: assert(false);
}
}
/**
* Returns a vector of `{ prime, index }`.
*/
std::vector<std::pair<int, int>> factorize(unsigned int n) const {
assert(0 < n and n <= N);
std::vector<std::pair<int, int>> prime_powers;
while (n > 1) {
int p = prime_factor(n), c = 0;
do { n /= p, ++c; } while (n % p == 0);
prime_powers.emplace_back(p, c);
}
return prime_powers;
}
/**
* Returns the divisors of `n`.
* It is NOT guaranteed that the returned vector is sorted.
*/
std::vector<int> divisors(unsigned int n) const {
assert(0 < n and n <= N);
std::vector<int> divs { 1 };
for (auto [prime, index] : factorize(n)) {
int sz = divs.size();
for (int i = 0; i < sz; ++i) {
int d = divs[i];
for (int j = 0; j < index; ++j) {
divs.push_back(d *= prime);
}
}
}
return divs;
}
};
template <unsigned int N>
unsigned int Sieve<N>::pf[Sieve<N>::base_max + internal::sieve::K];
} // namespace suisen
namespace suisen::fast_factorize {
namespace internal {
template <typename T>
constexpr int floor_log2(T n) {
int i = 0;
while (n) n >>= 1, ++i;
return i - 1;
}
template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
T pollard_rho(const T n) {
using M = safely_multipliable_t<T>;
const T m = T(1) << (floor_log2(n) / 5);
static std::mt19937_64 rng{std::random_device{}()};
std::uniform_int_distribution<T> dist(0, n - 1);
// const Montgomery64 mg{n};
while (true) {
T c = dist(rng);
auto f = [&](T x) -> T { return (M(x) * x + c) % n; };
T x, y = 2, ys, q = 1, g = 1;
for (T r = 1; g == 1; r <<= 1) {
x = y;
for (T i = 0; i < r; ++i) y = f(y);
for (T k = 0; k < r and g == 1; k += m) {
ys = y;
for (T i = 0; i < std::min(m, r - k); ++i) y = f(y), q = M(q) * (x > y ? x - y : y - x) % n;
g = std::gcd(q, n);
}
}
if (g == n) {
g = 1;
while (g == 1) ys = f(ys), g = std::gcd(x > ys ? x - ys : ys - x, n);
}
if (g < n) {
if (miller_rabin::is_prime(g)) return g;
if (T d = n / g; miller_rabin::is_prime(d)) return d;
return pollard_rho(g);
}
}
}
}
template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
std::vector<std::pair<T, int>> factorize(T n) {
static constexpr int threshold = 1000000;
static Sieve<threshold> sieve;
std::vector<std::pair<T, int>> res;
if (n <= threshold) {
for (auto [p, q] : sieve.factorize(n)) res.emplace_back(p, q);
return res;
}
if ((n & 1) == 0) {
int q = 0;
do ++q, n >>= 1; while ((n & 1) == 0);
res.emplace_back(2, q);
}
for (T p = 3; p * p <= n; p += 2) {
if (p >= 101 and n >= 1 << 20) {
while (n > 1) {
if (miller_rabin::is_prime(n)) {
res.emplace_back(std::exchange(n, 1), 1);
} else {
p = internal::pollard_rho(n);
int q = 0;
do ++q, n /= p; while (n % p == 0);
res.emplace_back(p, q);
}
}
break;
}
if (n % p == 0) {
int q = 0;
do ++q, n /= p; while (n % p == 0);
res.emplace_back(p, q);
}
}
if (n > 1) res.emplace_back(n, 1);
return res;
}
} // namespace suisen::fast_factorize
namespace suisen {
namespace internal::order_prime_mod {
template <int id>
struct mint64 {
static uint64_t mod() { return _mod; }
static void set_mod(uint64_t new_mod) { mint64<id>::_mod = new_mod; }
mint64() : _val(0) {}
mint64(long long val) : _val(safe_mod(val)) {}
uint64_t val() { return _val; }
friend mint64& operator*=(mint64& x, const mint64& y) {
x._val = __uint128_t(x._val) * y._val % _mod;
return x;
}
friend mint64 operator*(mint64 x, const mint64& y) {
x *= y;
return x;
}
mint64 pow(long long b) const {
assert(b >= 0);
mint64 p = *this, res = 1;
for (; b; b >>= 1) {
if (b & 1) res *= p;
p *= p;
}
return res;
}
private:
static inline uint64_t _mod;
uint64_t _val;
static uint64_t safe_mod(long long val) { return (val %= _mod) < 0 ? val + _mod : val; }
};
}
template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
struct OrderMod {
using U = std::make_unsigned_t<T>;
OrderMod() = default;
OrderMod(T m) : _mod(m) {
auto factorized = fast_factorize::factorize<T>(_mod);
_is_prime = factorized.size() == 1;
_lambda = _carmichael(factorized);
_phi = _totient(factorized);
for (auto [p, q] : fast_factorize::factorize<T>(_lambda)) {
U r = 1;
for (int i = 0; i < q; ++i) r *= p;
_fac_lambda.emplace_back(p, q, r);
}
}
bool is_primitive_root(U a) const {
if (_mod < 1ULL << 32) {
using mint = atcoder::dynamic_modint<1000000000>;
U old_mod = mint::mod();
mint::set_mod(_mod);
bool res = _is_primitive_root_impl<mint>(a);
mint::set_mod(old_mod);
return res;
} else {
using mint = internal::order_prime_mod::mint64<1000000000>;
U old_mod = mint::mod();
mint::set_mod(_mod);
bool res = _is_primitive_root_impl<mint>(a);
mint::set_mod(old_mod);
return res;
}
}
T primitive_root() const {
assert(_lambda == _phi);
if (_mod < 1ULL << 32) {
return _primitive_root_impl<std::mt19937>();
} else {
return _primitive_root_impl<std::mt19937_64>();
}
}
T operator()(U a) const {
if (_mod < 1ULL << 32) {
using mint = atcoder::dynamic_modint<1000000000>;
U old_mod = mint::mod();
mint::set_mod(_mod);
T res = _order_impl<mint>(a);
mint::set_mod(old_mod);
return res;
} else {
using mint = internal::order_prime_mod::mint64<1000000000>;
U old_mod = mint::mod();
mint::set_mod(_mod);
T res = _order_impl<mint>(a);
mint::set_mod(old_mod);
return res;
}
}
T mod() const {
return _mod;
}
T totient() const {
return _phi;
}
T carmichael() const {
return _lambda;
}
bool is_prime() const {
return _is_prime;
}
std::vector<T> carmichael_prime_factors() const {
std::vector<T> res;
for (const auto &e : _fac_lambda) res.push_back(std::get<0>(e));
return res;
}
private:
U _mod;
U _phi;
U _lambda;
bool _is_prime;
std::vector<std::tuple<U, int, U>> _fac_lambda;
static T _carmichael(const std::vector<std::pair<T, int>>& factorized) {
T lambda = 1;
for (auto [p, ep] : factorized) {
T phi = p - 1;
int exponent = ep - (1 + (p == 2 and ep >= 3));
for (int i = 0; i < exponent; ++i) phi *= p;
lambda = std::lcm(lambda, phi);
}
return lambda;
}
static T _totient(const std::vector<std::pair<T, int>>& factorized) {
T t = 1;
for (const auto& [p, ep] : factorized) {
t *= p - 1;
for (int i = 0; i < ep - 1; ++i) t *= p;
}
return t;
}
template <typename mint>
bool _is_primitive_root_impl(U a) const {
if (_lambda != _phi) return false;
if (_mod == 2) return a % 2 == 1;
const int k = _fac_lambda.size();
U x = _lambda;
for (const auto& [p, q, pq] : _fac_lambda) x /= p;
mint b = mint(a).pow(x);
if (k == 1) return b.val() != 1;
auto dfs = [&](auto dfs, const int l, const int r, const mint val) -> bool {
const int m = (l + r) >> 1;
U lp = 1;
for (int i = m; i < r; ++i) lp *= std::get<0>(_fac_lambda[i]);
mint lval = val.pow(lp);
if (m - l == 1) {
if (lval.val() == 1) return false;
} else {
if (not dfs(dfs, l, m, lval)) return false;
}
U rp = 1;
for (int i = l; i < m; ++i) rp *= std::get<0>(_fac_lambda[i]);
mint rval = val.pow(rp);
if (r - m == 1) {
if (rval.val() == 1) return false;
} else {
if (not dfs(dfs, m, r, rval)) return false;
}
return true;
};
return dfs(dfs, 0, k, b);
}
template <typename Rng>
T _primitive_root_impl() const {
if (_mod == 2) return 1;
Rng rng{ std::random_device{}() };
while (true) {
U a = rng() % (_mod - 2) + 2;
while (not _is_prime and std::gcd(a, _mod) != 1) {
a = rng() % (_mod - 2) + 2;
}
if (is_primitive_root(a)) return a;
}
}
template <typename mint>
U _order_impl(U a) const {
if (_mod == 2) return a % 2 == 1;
const int k = _fac_lambda.size();
U res = 1;
auto update = [&](U p, mint val) {
while (val.val() != 1) {
val = val.pow(p);
res *= p;
}
};
if (k == 1) {
update(std::get<0>(_fac_lambda.front()), a);
return res;
}
auto dfs = [&](auto dfs, const int l, const int r, const mint val) -> void {
const int m = (l + r) >> 1;
U lp = 1;
for (int i = m; i < r; ++i) lp *= std::get<2>(_fac_lambda[i]);
mint lval = val.pow(lp);
if (m - l == 1) {
update(std::get<0>(_fac_lambda[l]), lval);
} else {
dfs(dfs, l, m, lval);
}
U rp = 1;
for (int i = l; i < m; ++i) rp *= std::get<2>(_fac_lambda[i]);
mint rval = val.pow(rp);
if (r - m == 1) {
update(std::get<0>(_fac_lambda[m]), rval);
} else {
dfs(dfs, m, r, rval);
}
};
dfs(dfs, 0, k, a);
return res;
}
};
} // namespace suisen
#include <unordered_map>
namespace suisen {
namespace internal::discrete_logarithm {
int floor_log2(int m) {
int res = 0;
while (1 << (res + 1) <= m) ++res;
return res;
}
}
template <typename mint>
int discrete_logarithm_coprime(mint x, mint y) {
const int m = mint::mod();
if (y == 1 or m == 1) return 0;
if (x == 0) return y == 0 ? 1 : -1;
const int p = ::sqrt(m) + 1;
mint a = mint(x).inv().pow(p);
std::unordered_map<int, int> mp;
mint pow_x = 1;
for (int j = 0; j < p; ++j, pow_x *= x) mp.try_emplace(pow_x.val(), j);
mint ya = y;
for (int i = 0; i < p; ++i, ya *= a) {
if (auto it = mp.find(ya.val()); it != mp.end()) return p * i + it->second;
}
return -1;
}
template <typename mint>
int discrete_logarithm(mint x, mint y) {
using namespace internal::discrete_logarithm;
const int m = mint::mod();
if (m == 1) return 0;
const int d = floor_log2(m);
mint pow_x = 1;
for (int i = 0; i < d; ++i, pow_x *= x) if (pow_x == y) return i;
const int g = std::gcd(pow_x.val(), m);
if (y.val() % g) return -1;
mint::set_mod(m / g);
const int t = discrete_logarithm_coprime(mint(x.val()), mint(y.val()) * mint(pow_x.val()).inv());
mint::set_mod(m);
return t != -1 ? d + t : -1;
}
} // namespace suisen
namespace suisen {
namespace internal::index_calculus {
template <typename mint>
struct SystemOfLinearEquations {
SystemOfLinearEquations() = default;
SystemOfLinearEquations(int target_var_id) : target_var_id(target_var_id) {}
void append(std::vector<mint> r, mint bi) {
int ti = target_var_id + 1;
for (int i = 0; i <= target_var_id; ++i) if (r[i] != 0) {
ti = i;
break;
}
if (ti > target_var_id) return;
const int l = A.size();
for (int i = 0; i < l; ++i) {
eliminate(top_pos[i], A[i], b[i], ti, r, bi);
if (ti > target_var_id) return;
}
A.push_back(std::move(r));
top_pos.push_back(ti);
b.push_back(bi);
}
void append(const std::vector<std::pair<int, mint>>& ri, mint bi) {
std::vector<mint> r(target_var_id + 1);
for (auto [j, v] : ri) r[j] = v;
append(r, bi);
}
std::optional<mint> target() {
if (top_pos.empty() or top_pos.back() != target_var_id) return std::nullopt;
auto [g, inv_c] = atcoder::internal::inv_gcd(A.back().back().val(), mint::mod());
return g == 1 ? std::make_optional(b.back() * inv_c) : std::nullopt;
}
void change_target() {
const int l = A.size();
int t = -1;
for (int i = l - 1; i >= 0; --i) {
if (A[i][target_var_id] != 0) {
t = i;
break;
}
}
SystemOfLinearEquations<mint> nxt(target_var_id);
for (int i = l - 1; i > t; --i) {
nxt.append(A[i], b[i]);
}
for (int i = t - 1; i >= 0; --i) {
if (A[i][target_var_id] != 0) {
const auto T = euclid(A[t][target_var_id].val(), A[i][target_var_id].val());
for (int col = top_pos[i]; col <= target_var_id; ++col) {
apply_euclid(T, A[t][col], A[i][col]);
}
apply_euclid(T, b[t], b[i]);
}
nxt.append(A[i], b[i]);
}
*this = std::move(nxt);
}
private:
int target_var_id;
std::vector<std::vector<mint>> A;
std::vector<int> top_pos;
std::vector<mint> b;
// Euclidean Algorithm
// A * [a, b] = [gcd(a,b), 0]
static std::array<std::array<int, 2>, 2> euclid(int a, int b) {
int x = 1, y = 0, z = 0, w = 1;
while (b) {
int p = a / b, q = a % b;
x -= p * z, std::swap(x, z);
y -= p * w, std::swap(y, w);
a = b, b = q;
}
return { x, y, z, w };
}
static void apply_euclid(const std::array<std::array<int, 2>, 2>& A, mint& x, mint& y) {
mint x2 = x, y2 = y;
x = A[0][0] * x2 + A[0][1] * y2;
y = A[1][0] * x2 + A[1][1] * y2;
}
static void eliminate(int& ti, std::vector<mint>& ri, mint& bi, int& tj, std::vector<mint>& rj, mint& bj) {
if (ti != tj) {
if (ti > tj) std::swap(ti, tj), std::swap(ri, rj), std::swap(bi, bj);
return;
}
const int siz = ri.size();
assert(int(rj.size()) == siz);
const auto T = euclid(ri[ti].val(), rj[tj].val());
for (int col = ti; col < siz; ++col) {
apply_euclid(T, ri[col], rj[col]);
}
apply_euclid(T, bi, bj);
while (tj < siz and rj[tj] == 0) ++tj;
}
};
}
// mod prime only.
struct IndexCalculus {
private:
using mint = atcoder::dynamic_modint<73495793>;
using mint2 = atcoder::dynamic_modint<73495794>;
public:
IndexCalculus() = default;
IndexCalculus(const OrderMod<int>& ord) : _p(ord.mod()), _ord(ord) {};
int discrete_log(int a, int b, int p) {
int old_mod = mint::mod(), old_mod2 = mint2::mod();
mint::set_mod(p), mint2::set_mod(p - 1);
int res = discrete_log_impl(a, b, p);
mint::set_mod(old_mod), mint2::set_mod(old_mod2);
return res;
}
private:
static constexpr uint32_t primes[60]{
2, 3, 5, 7, 11, 13, 17, 19, 23, 29,
31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
73, 79, 83, 89, 97, 101, 103, 107, 109, 113,
127, 131, 137, 139, 149, 151, 157, 163, 167, 173,
179, 181, 191, 193, 197, 199, 211, 223, 227, 229,
233, 239, 241, 251, 257, 263, 269, 271, 277, 281,
};
// inv_primes[i] = ceil(2^32 / primes[i])
static constexpr uint32_t inv_primes[60]{
2147483648, 1431655766, 858993460, 613566757, 390451573, 330382100, 252645136, 226050911, 186737709, 148102321,
138547333, 116080198, 104755300, 99882961, 91382283, 81037119, 72796056, 70409300, 64103990, 60492498,
58835169, 54366675, 51746594, 48258060, 44278014, 42524429, 41698712, 40139882, 39403370, 38008561,
33818641, 32786010, 31350127, 30899046, 28825284, 28443493, 27356480, 26349493, 25718368, 24826401,
23994231, 23729102, 22486740, 22253717, 21801865, 21582751, 20355296, 19259944, 18920561, 18755316,
18433337, 17970575, 17821442, 17111424, 16711936, 16330675, 15966422, 15848588, 15505298, 15284582,
};
int _p = -1;
OrderMod<int> _ord;
int _a = -1;
internal::index_calculus::SystemOfLinearEquations<mint2> _eq;
static int safe_mod(int a, int p) { return ((a %= p) < 0) ? a + p : a; }
static int discrete_log_naive(mint a, mint b) {
mint pow_a = 1;
for (int res = 0; res < int(mint::mod()) - 1; ++res) {
if (pow_a == b) return res;
pow_a *= a;
}
return -1;
}
static std::optional<std::vector<std::pair<int, mint2>>> try_factorize(const int B, uint32_t v) {
assert(B <= 60);
std::vector<std::pair<int, mint2>> res;
for (int i = 0; i < B; ++i) {
const uint32_t m = primes[B - i - 1], im = inv_primes[B - i - 1];
if (uint32_t q = (uint64_t(v) * im) >> 32; v == q * m) {
// q = floor(v/m)
int c = 0;
do v = q, q = (uint64_t(v) * im) >> 32, ++c; while (v == q * m);
res.emplace_back(i, mint2::raw(c));
}
}
return v == 1 ? std::make_optional(std::move(res)) : std::nullopt;
}
int discrete_log_impl(int a, int b, int p) {
a = safe_mod(a, p), b = safe_mod(b, p);
if (b == 0) return a == 0 ? 1 : -1;
if (b == 1) return 0;
if (a == 0) return -1;
if (a == 1) return -1;
if (p <= 64) {
return discrete_log_naive(a, b);
}
const int B = ::pow(p - 1, 1 / (2 * ::sqrt(::log(p - 1) / ::log(::log(p - 1)))));
assert(B <= 60);
if (p != _p) {
_p = p, _ord = OrderMod<int>(p);
_a = a, _eq = internal::index_calculus::SystemOfLinearEquations<mint2>(B);
} else if (a != _a) {
_a = a, _eq = internal::index_calculus::SystemOfLinearEquations<mint2>(B);
} else {
_eq.change_target();
}
assert(_ord.is_prime());
const int ord_a = _ord(a), ord_b = _ord(b);
if (ord_a % ord_b) return -1;
static std::mt19937 rng{};
while (true) {
const int k = rng() % ord_a;
auto opt_fac = try_factorize(B, (mint(a).pow(k) * b).val());
if (not opt_fac) continue;
auto& fac = *opt_fac;
fac.emplace_back(B, -1);
_eq.append(std::move(fac), k);
if (auto opt_res = _eq.target()) return opt_res->val() % _ord(a);
}
}
};
namespace internal::pohlig_hellman {
using mint = atcoder::dynamic_modint<73495793>;
int naive(int a, int b, int n) {
mint pow_a = 1;
for (int res = 0; res < n; ++res) {
if (pow_a == b) return res;
pow_a *= a;
}
return -1;
}
int pohlig_hellman_prime_power_bsgs(int a, int b, int n, int p, int q) {
const mint gamma = mint(a).pow(n / p);
const mint inv_a = mint(a).inv();
int x = 0;
for (int k = 0, pl = 1, pr = n; k < q; ++k) {
pr /= p;
int d = suisen::discrete_logarithm_coprime(gamma, (inv_a.pow(x) * b).pow(pr));
if (d == -1) return -1;
x += pl * d;
pl *= p;
}
return x;
}
int pohlig_hellman_prime_power_index_calculus(int a, int b, int n, int p, int q, const OrderMod<int>& ord) {
const mint gamma = mint(a).pow(n / p);
const mint inv_a = mint(a).inv();
IndexCalculus ic{ ord };
int x = 0;
for (int k = 0, pl = 1, pr = n; k < q; ++k) {
pr /= p;
int d = ic.discrete_log(gamma.val(), (inv_a.pow(x) * b).pow(pr).val(), ord.mod());
x += pl * d;
pl *= p;
}
return x;
}
int pohlig_hellman(int a, int b, int p, int q, const OrderMod<int> &ord) {
// gcd(a, p) = 1
if (b == 1) return 0;
if (a == 1) return b == 1 ? 0 : -1;
if (b % p == 0) return -1;
if (q == 1) return IndexCalculus{ ord }.discrete_log(a, b, p);
const int pq = ord.mod();
const int n = ord(a);
if (n <= 64) return naive(a, b, pq);
if (n % ord(b)) return -1;
const std::vector<std::pair<int, int>> fac_n = [&] {
std::vector<std::pair<int, int>> res;
int n2 = n;
for (int p : ord.carmichael_prime_factors()) if (n2 % p == 0) {
int& c = res.emplace_back(p, 0).second;
do n2 /= p, ++c; while (n2 % p == 0);
}
return res;
}();
std::vector<long long> rs, ms;
for (auto [p, q] : fac_n) {
int pq = 1;
for (int i = 0; i < q; ++i) pq *= p;
int na = mint(a).pow(n / pq).val(), nb = mint(b).pow(n / pq).val();
int x;
if (pq <= 64) {
x = naive(na, nb, pq);
} else if (ord.is_prime()) {
x = pohlig_hellman_prime_power_index_calculus(na, nb, pq, p, q, ord);
} else {
x = pohlig_hellman_prime_power_bsgs(na, nb, pq, p, q);
}
if (x == -1) return -1;
rs.push_back(x), ms.push_back(pq);
}
return atcoder::crt(rs, ms).first;
}
int discrete_logarithm_crt(int a, int b, int m) {
assert(std::gcd(a, m) == 1);
long long r = 0, md = 1;
for (auto [p, q] : fast_factorize::factorize(m)) {
int pq = 1;
for (int i = 0; i < q; ++i) pq *= p;
mint::set_mod(pq);
OrderMod ord(pq);
const long long r2 = pohlig_hellman(a % pq, b % pq, p, q, ord);
if (r2 == -1) return -1;
const long long md2 = ord(a);
std::tie(r, md) = atcoder::crt({ r, r2 }, { md, md2 });
if (md == 0) return -1;
}
return r;
}
int floor_log2(int m) {
int res = 0;
while (1 << (res + 1) <= m) ++res;
return res;
}
int discrete_logarithm(int a, int b, int m) {
if (m == 1 or b == 1) return 0;
if (a == 0) return b == 0 ? 1 : b == 1 ? 0 : -1;
if (a == 1) return b == 1 ? 0 : -1;
const int d = floor_log2(m);
mint pow_x = 1;
for (int i = 0; i < d; ++i, pow_x *= a) if (pow_x == b) return i;
const int g = std::gcd(pow_x.val(), m);
if (b % g) return -1;
mint::set_mod(m / g);
const int t = discrete_logarithm_crt(mint(a).val(), (mint(b) / pow_x.val()).val(), m / g);
return t != -1 ? d + t : -1;
}
}
int discrete_logarithm_fast(int a, int b, int m) {
if ((a %= m) < 0) a += m;
if ((b %= m) < 0) b += m;
int old_mod = internal::pohlig_hellman::mint::mod();
internal::pohlig_hellman::mint::set_mod(m);
int res = internal::pohlig_hellman::discrete_logarithm(a, b, m);
internal::pohlig_hellman::mint::set_mod(old_mod);
return res;
}
} // namespace suisen
str ts(mint s) { return ts(s.v); }
str ts(mint1 s) { return ts(s.v); }
void solve() {
int n; re(n);
vector<mint> v(n);
for (int i = 0; i < n; i++) {
int x; re(x); v[i] = x;
}
string s;
re(s);
Poly<mint1> stars(n-1);
for (int i = 0; i < n-1; i++) stars[i]=(s[i]=='-');
Poly<mint1> dlog(n-1);
for (int i = 1; i < n; i++) dlog[i-1] = -suisen::discrete_logarithm_fast(3,i,base.mod);
for (int i = n-2; i >= 2; i--) dlog[i] -= dlog[i-2];
dlog[0] += suisen::discrete_logarithm_fast(3,base.mod-1,base.mod);
Poly<mint1> den = stars * dlog;
mint ans = 0;
for (int i = 0; i < n; i++) {
mint prod;
if (i>=2 && s[i-2]=='-') prod=0;
else if (i == 0) prod = 1;
else prod = mint(3).pow(den[i-1].v);
//if (i>=1) dbg(i, prod, den[i-1]);
mint prob = (1 + prod) / 2;
ans += (2*prob - 1) * v[i];
}
for (int i = 1; i <= n-1; i++) {
ans *= mint(i);
}
ps(ans.v);
}
詳細信息
answer.code:2304:18: error: ‘optional’ in namespace ‘std’ does not name a template type
2304 | std::optional<mint> target() {
| ^~~~~~~~
answer.code:1506:1: note: ‘std::optional’ is defined in header ‘<optional>’; did you forget to ‘#include <optional>’?
1505 | #include <iterator>
+++ |+#include <optional>
1506 | #include <tuple>
answer.code:2433:21: error: ‘optional’ in namespace ‘std’ does not name a template type
2433 | static std::optional<std::vector<std::pair<int, mint2>>> try_factorize(const int B, uint32_t v) {
| ^~~~~~~~
answer.code:2433:16: note: ‘std::optional’ is defined in header ‘<optional>’; did you forget to ‘#include <optional>’?
2433 | static std::optional<std::vector<std::pair<int, mint2>>> try_factorize(const int B, uint32_t v) {
| ^~~
answer.code: In member function ‘int suisen::IndexCalculus::discrete_log_impl(int, int, int)’:
answer.code:2480:32: error: ‘try_factorize’ was not declared in this scope; did you mean ‘fast_factorize’?
2480 | auto opt_fac = try_factorize(B, (mint(a).pow(k) * b).val());
| ^~~~~~~~~~~~~
| fast_factorize
answer.code:2485:40: error: ‘struct suisen::internal::index_calculus::SystemOfLinearEquations<atcoder::dynamic_modint<73495794> >’ has no member named ‘target’
2485 | if (auto opt_res = _eq.target()) return opt_res->val() % _ord(a);
| ^~~~~~