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ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#836646 | #9923. Ma Meilleure Ennemie | ucup-team159# | TL | 1ms | 3740kb | C++20 | 9.5kb | 2024-12-29 03:15:44 | 2024-12-29 03:15:45 |
Judging History
answer
#line 1 "I.cpp"
// #pragma GCC target("avx2,avx512f,avx512vl,avx512bw,avx512dq,avx512cd,avx512vbmi,avx512vbmi2,avx512vpopcntdq,avx512bitalg,bmi,bmi2,lzcnt,popcnt")
#pragma GCC optimize("Ofast")
#line 2 "/home/sigma/comp/library/template.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using uint = unsigned int;
using ull = unsigned long long;
#define rep(i,n) for(int i=0;i<int(n);i++)
#define rep1(i,n) for(int i=1;i<=int(n);i++)
#define per(i,n) for(int i=int(n)-1;i>=0;i--)
#define per1(i,n) for(int i=int(n);i>0;i--)
#define all(c) c.begin(),c.end()
#define si(x) int(x.size())
#define pb push_back
#define eb emplace_back
#define fs first
#define sc second
template<class T> using V = vector<T>;
template<class T> using VV = vector<vector<T>>;
template<class T,class U> bool chmax(T& x, U y){
if(x<y){ x=y; return true; }
return false;
}
template<class T,class U> bool chmin(T& x, U y){
if(y<x){ x=y; return true; }
return false;
}
template<class T> void mkuni(V<T>& v){sort(all(v));v.erase(unique(all(v)),v.end());}
template<class T> int lwb(const V<T>& v, const T& a){return lower_bound(all(v),a) - v.begin();}
template<class T>
V<T> Vec(size_t a) {
return V<T>(a);
}
template<class T, class... Ts>
auto Vec(size_t a, Ts... ts) {
return V<decltype(Vec<T>(ts...))>(a, Vec<T>(ts...));
}
template<class S,class T> ostream& operator<<(ostream& o,const pair<S,T> &p){
return o<<"("<<p.fs<<","<<p.sc<<")";
}
template<class T> ostream& operator<<(ostream& o,const vector<T> &vc){
o<<"{";
for(const T& v:vc) o<<v<<",";
o<<"}";
return o;
}
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n-1); }
#ifdef LOCAL
#define show(x) cerr << "LINE" << __LINE__ << " : " << #x << " = " << (x) << endl
void dmpr(ostream& os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
os<<t<<" ~ ";
dmpr(os,args...);
}
#define shows(...) cerr << "LINE" << __LINE__ << " : ";dmpr(cerr,##__VA_ARGS__)
#define dump(x) cerr << "LINE" << __LINE__ << " : " << #x << " = {"; \
for(auto v: x) cerr << v << ","; cerr << "}" << endl;
#else
#define show(x) void(0)
#define dump(x) void(0)
#define shows(...) void(0)
#endif
template<class D> D divFloor(D a, D b){
return a / b - (((a ^ b) < 0 && a % b != 0) ? 1 : 0);
}
template<class D> D divCeil(D a, D b) {
return a / b + (((a ^ b) > 0 && a % b != 0) ? 1 : 0);
}
#line 1 "/home/sigma/comp/library/math/mint.cpp"
/*
任意mod なら
template なくして costexpr の行消して global に unsigned int mod = 1;
で cin>>mod してから使う
任意 mod はかなり遅いので、できれば "atcoder/modint" を使う
*/
template<unsigned int mod_>
struct ModInt{
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
constexpr static uint mod = mod_;
uint v;
ModInt():v(0){}
ModInt(ll _v):v(normS(_v%mod+mod)){}
explicit operator bool() const {return v!=0;}
static uint normS(const uint &x){return (x<mod)?x:x-mod;} // [0 , 2*mod-1] -> [0 , mod-1]
static ModInt make(const uint &x){ModInt m; m.v=x; return m;}
ModInt operator+(const ModInt& b) const { return make(normS(v+b.v));}
ModInt operator-(const ModInt& b) const { return make(normS(v+mod-b.v));}
ModInt operator-() const { return make(normS(mod-v)); }
ModInt operator*(const ModInt& b) const { return make((ull)v*b.v%mod);}
ModInt operator/(const ModInt& b) const { return *this*b.inv();}
ModInt& operator+=(const ModInt& b){ return *this=*this+b;}
ModInt& operator-=(const ModInt& b){ return *this=*this-b;}
ModInt& operator*=(const ModInt& b){ return *this=*this*b;}
ModInt& operator/=(const ModInt& b){ return *this=*this/b;}
ModInt& operator++(int){ return *this=*this+1;}
ModInt& operator--(int){ return *this=*this-1;}
template<class T> friend ModInt operator+(T a, const ModInt& b){ return (ModInt(a) += b);}
template<class T> friend ModInt operator-(T a, const ModInt& b){ return (ModInt(a) -= b);}
template<class T> friend ModInt operator*(T a, const ModInt& b){ return (ModInt(a) *= b);}
template<class T> friend ModInt operator/(T a, const ModInt& b){ return (ModInt(a) /= b);}
ModInt pow(ll p) const {
if(p<0) return inv().pow(-p);
ModInt a = 1;
ModInt x = *this;
while(p){
if(p&1) a *= x;
x *= x;
p >>= 1;
}
return a;
}
ModInt inv() const { // should be prime
return pow(mod-2);
}
// ll extgcd(ll a,ll b,ll &x,ll &y) const{
// ll p[]={a,1,0},q[]={b,0,1};
// while(*q){
// ll t=*p/ *q;
// rep(i,3) swap(p[i]-=t*q[i],q[i]);
// }
// if(p[0]<0) rep(i,3) p[i]=-p[i];
// x=p[1],y=p[2];
// return p[0];
// }
// ModInt inv() const {
// ll x,y;
// extgcd(v,mod,x,y);
// return make(normS(x+mod));
// }
bool operator==(const ModInt& b) const { return v==b.v;}
bool operator!=(const ModInt& b) const { return v!=b.v;}
bool operator<(const ModInt& b) const { return v<b.v;}
friend istream& operator>>(istream &o,ModInt& x){
ll tmp;
o>>tmp;
x=ModInt(tmp);
return o;
}
friend ostream& operator<<(ostream &o,const ModInt& x){ return o<<x.v;}
// friend ostream& operator<<(ostream &o,const ModInt& x){
// for(int b=1;b<=1000;b++){
// ModInt ib = ModInt(b).inv();
// for(int a=-1000;a<=1000;a++){
// if(ModInt(a) * ib == x){
// return o << a << "/" << b;
// }
// }
// }
// return o<<x.v;
// }
};
using mint = ModInt<998244353>;
//using mint = ModInt<1000000007>;
V<mint> fact,ifact,invs;
// a,b >= 0 のみ
mint Choose(int a,int b){
if(b<0 || a<b) return 0;
return fact[a] * ifact[b] * ifact[a-b];
}
/*
// b >= 0 の範囲で、 Choose(a,b) = a(a-1)..(a-b+1) / b!
mint Choose(int a,int b){
if(b<0 || a<b) return 0;
return fact[a] * ifact[b] * ifact[a-b];
}
*/
void InitFact(int N){ //[0,N]
N++;
fact.resize(N);
ifact.resize(N);
invs.resize(N);
fact[0] = 1;
rep1(i,N-1) fact[i] = fact[i-1] * i;
ifact[N-1] = fact[N-1].inv();
for(int i=N-2;i>=0;i--) ifact[i] = ifact[i+1] * (i+1);
rep1(i,N-1) invs[i] = fact[i-1] * ifact[i];
}
#line 1 "/home/sigma/comp/library/math/factorization.hpp"
/*
素因数分解 1 <= n <= 10^18
pollard_rho's algorithm
O(n^0.25 polylog(n)) くらいらしい
*/
template<class T>
T gcd(T a,T b){
a = abs(a), b = abs(b);
if(b==0) return a;
return gcd(b,a%b);
}
template<class T, class U>
T pow_mod(T x, U p, T mod){
assert(p>=0);
x %= mod;
T a = 1 % mod;
while(p){
if(p&1) a = a*x%mod;
x = x*x%mod;
p >>= 1;
}
return a;
}
using ll = long long;
bool isprime(ll n){
if(n<=1) return 0;
if(n==2) return 1;
if(n%2==0) return 0;
ll d = n-1;
while(d%2==0) d/=2;
static const vector<ll> alist{2,3,5,7,11,13,17,19,23,29,31,37};
for(ll a: alist){
if(n<=a) break;
ll t = d;
ll y = pow_mod<__int128>(a,t,n);
while(t!=n-1 && y!=1 && y!=n-1){
y = __int128(y)*y%n;
t<<=1;
}
if(y!=n-1 && t%2==0) return 0;
}
return 1;
}
ll pollard_single(ll n){
if(isprime(n)) return n;
if(!(n&1)) return 2;
ll ph,x,y,p;
auto f = [&](ll x, ll n){ return (__int128(x)*x+ph)%n; };
for(ph=1;;ph++){
x=ph; y=f(x,n); p=gcd(y-x,n);
while(p==1){
x=f(x,n); y=f(f(y,n),n); p=gcd((y-x+n)%n,n)%n;
}
if(p==0 || p==n) continue;
return p;
}
assert(0);
}
vector<ll> pollard(ll n){
if(n==1) return {};
ll x = pollard_single(n);
if(x==n) return {x};
vector<ll> le = pollard(x);
vector<ll> ri = pollard(n/x);
for(ll d: ri) le.push_back(d);
sort(all(le));
return le;
}
vector<pair<long long,int>> factorize(ll n){
auto ps = pollard(n);
sort(all(ps));
map<ll,int> mp;
for(ll p: ps) mp[p]++;
vector<pair<ll,int>> res;
for(auto [p,r]: mp) res.emplace_back(p,r);
return res;
}
ll totient(ll n){
auto v = pollard(n);
map<ll,int> mp; for(ll p: v) mp[p]++;
ll phi = 1;
for(auto [p,r]: mp){
for(int _=0;_<r-1;_++) phi *= p;
phi *= p-1;
}
return phi;
}
#line 7 "I.cpp"
int main(){
cin.tie(0);
ios::sync_with_stdio(false); //DON'T USE scanf/printf/puts !!
cout << fixed << setprecision(20);
ll N,X; cin >> N >> X;
V<ll> ms;
V<ll> c;
VV<int> to,sgn;
{
auto qs = factorize(N);
V<int> coef(si(qs),1);
{
rep(i,si(qs)-1) coef[i+1] = coef[i] * (qs[si(qs)-1-i].sc+1);
reverse(all(coef));
}
V<ll> coefsm(1<<si(qs));
{
rep(s,1<<si(qs)){
rep(i,si(qs)) if(s>>i&1) coefsm[s] += coef[i];
}
}
show(coef);
show(coefsm);
auto dfs = [&](auto& self, ll v, int i, int s, int idx){
if(i == si(qs)){
ms.pb(v);
V<int> toi,sgni;
show("------");
show(v);show(idx);
for(int t=s;t>0;t=(t-1)&s){
toi.pb(idx + coefsm[t]);
show(idx+coefsm[t]);
sgni.pb(__builtin_popcount(t)&1 ? 1 : -1);
}
to.eb(toi); sgn.eb(sgni);
return;
}
rep(j,qs[i].sc+1){
self(self, v, i+1, s|(j == qs[i].sc ? 0 : 1<<i), idx + j * coef[i]);
if(j == qs[i].sc) break;
v *= qs[i].fs;
}
};
dfs(dfs, 1, 0, 0, 0);
}
show(ms);
show(to);
show(sgn);
int M = si(ms);
{
c.resize(M);
rep(i,M){
ll m = ms[i];
c[i] = X/m;
show("--------");
show(m);
rep(jj,si(to[i])){
int j = to[i][jj];
ll mj = ms[j];
show(mj);
int s = sgn[i][jj];
show(s);
if(s == 1) c[i] -= X/mj;
else c[i] += X/mj;
}
}
}
show(c);
V<mint> f(si(ms));
per(i,si(ms)){
ll m = ms[i];
f[i] = c[i];
rep(jj,si(to[i])){
int j = to[i][jj];
ll mj = ms[j];
int s = sgn[i][jj];
if(s == 1) f[i] += f[j].pow(mj/m);
else f[i] -= f[j].pow(mj/m);
}
}
show(f);
cout << f[0] << endl;
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 0ms
memory: 3740kb
input:
4 4
output:
6
result:
ok 1 number(s): "6"
Test #2:
score: 0
Accepted
time: 1ms
memory: 3584kb
input:
2338 1470
output:
18530141
result:
ok 1 number(s): "18530141"
Test #3:
score: -100
Time Limit Exceeded
input:
941958815880242160 945059392259579928