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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 |
---|---|---|---|---|---|---|---|---|---|
#841424 | #9923. Ma Meilleure Ennemie | ucup-team3586# | TL | 1136ms | 6704kb | C++23 | 7.0kb | 2025-01-03 18:54:46 | 2025-01-03 18:54:46 |
Judging History
answer
#include<bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,tune=native")
uint64_t gcd_stein_impl( uint64_t x, uint64_t y ) {
if( x == y ) { return x; }
const uint64_t a = y - x;
const uint64_t b = x - y;
const int n = __builtin_ctzll( b );
const uint64_t s = x < y ? a : b;
const uint64_t t = x < y ? x : y;
return gcd_stein_impl( s >> n, t );
}
uint64_t gcd_stein( uint64_t x, uint64_t y ) {
if( x == 0 ) { return y; }
if( y == 0 ) { return x; }
const int n = __builtin_ctzll( x );
const int m = __builtin_ctzll( y );
return gcd_stein_impl( x >> n, y >> m ) << ( n < m ? n : m );
}
// ---- is_prime ----
uint64_t mod_pow( uint64_t x, uint64_t y, uint64_t mod ) {
uint64_t ret = 1;
uint64_t acc = x;
for( ; y; y >>= 1 ) {
if( y & 1 ) {
ret = __uint128_t(ret) * acc % mod;
}
acc = __uint128_t(acc) * acc % mod;
}
return ret;
}
bool miller_rabin( uint64_t n, const std::initializer_list<uint64_t>& as ) {
return std::all_of( as.begin(), as.end(), [n]( uint64_t a ) {
if( n <= a ) { return true; }
int e = __builtin_ctzll( n - 1 );
uint64_t z = mod_pow( a, ( n - 1 ) >> e, n );
if( z == 1 || z == n - 1 ) { return true; }
while( --e ) {
z = __uint128_t(z) * z % n;
if( z == 1 ) { return false; }
if( z == n - 1 ) { return true; }
}
return false;
});
}
bool is_prime( uint64_t n ) {
if( n == 2 ) { return true; }
if( n % 2 == 0 ) { return false; }
if( n < 4759123141 ) { return miller_rabin( n, { 2, 7, 61 } ); }
return miller_rabin( n, { 2, 325, 9375, 28178, 450775, 9780504, 1795265022 } );
}
// ---- Montgomery ----
class Montgomery {
uint64_t mod;
uint64_t R;
public:
Montgomery( uint64_t n ) : mod(n), R(n) {
for( size_t i = 0; i < 5; ++i ) {
R *= 2 - mod * R;
}
}
uint64_t fma( uint64_t a, uint64_t b, uint64_t c ) const {
const __uint128_t d = __uint128_t(a) * b;
const uint64_t e = c + mod + ( d >> 64 );
const uint64_t f = uint64_t(d) * R;
const uint64_t g = ( __uint128_t(f) * mod ) >> 64;
return e - g;
}
uint64_t mul( uint64_t a, uint64_t b ) const {
return fma( a, b, 0 );
}
};
// ---- Pollard's rho algorithm ----
uint64_t pollard_rho( uint64_t n ) {
if( n % 2 == 0 ) { return 2; }
const Montgomery m( n );
constexpr uint64_t C1 = 1;
constexpr uint64_t C2 = 2;
constexpr uint64_t M = 512;
uint64_t Z1 = 1;
uint64_t Z2 = 2;
retry:
uint64_t z1 = Z1;
uint64_t z2 = Z2;
for( size_t k = M; ; k *= 2 ) {
const uint64_t x1 = z1 + n;
const uint64_t x2 = z2 + n;
for( size_t j = 0; j < k; j += M ) {
const uint64_t y1 = z1;
const uint64_t y2 = z2;
uint64_t q1 = 1;
uint64_t q2 = 2;
z1 = m.fma( z1, z1, C1 );
z2 = m.fma( z2, z2, C2 );
for( size_t i = 0; i < M; ++i ) {
const uint64_t t1 = x1 - z1;
const uint64_t t2 = x2 - z2;
z1 = m.fma( z1, z1, C1 );
z2 = m.fma( z2, z2, C2 );
q1 = m.mul( q1, t1 );
q2 = m.mul( q2, t2 );
}
q1 = m.mul( q1, x1 - z1 );
q2 = m.mul( q2, x2 - z2 );
const uint64_t q3 = m.mul( q1, q2 );
const uint64_t g3 = gcd_stein( n, q3 );
if( g3 == 1 ) { continue; }
if( g3 != n ) { return g3; }
const uint64_t g1 = gcd_stein( n, q1 );
const uint64_t g2 = gcd_stein( n, q2 );
const uint64_t C = g1 != 1 ? C1 : C2;
const uint64_t x = g1 != 1 ? x1 : x2;
uint64_t z = g1 != 1 ? y1 : y2;
uint64_t g = g1 != 1 ? g1 : g2;
if( g == n ) {
do {
z = m.fma( z, z, C );
g = gcd_stein( n, x - z );
} while( g == 1 );
}
if( g != n ) {
return g;
}
Z1 += 2;
Z2 += 2;
goto retry;
}
}
}
void factorize_impl( uint64_t n, std::vector<uint64_t>& ret ) {
if( n <= 1 ) { return; }
if( is_prime( n ) ) { ret.push_back( n ); return; }
const uint64_t p = pollard_rho( n );
factorize_impl( p, ret );
factorize_impl( n / p, ret );
}
std::vector<uint64_t> factorize( uint64_t n ) {
std::vector<uint64_t> ret;
factorize_impl( n, ret );
std::sort( ret.begin(), ret.end() );
return ret;
}
using namespace std;
#define int long long
inline int read(){
int s=0,w=1;
char ch=getchar();
while(ch<'0'||ch>'9'){if(ch=='-')w=-1;ch=getchar();}
while(ch>='0'&&ch<='9') s=s*10+ch-'0',ch=getchar();
return s*w;
}
const int p=998244353;
int qp(int x,int y)
{
int res=1;
for(int t=x; y; y>>=1,t=1ll*t*t%p)
if(y&1) res=1ll*res*t%p;
return res;
}
int pr[103],k[103],idx[103],sz;
int n=read(),m=read();
int f[1<<20],g[1<<20];
void dfs(int x,int y,int z,int px)
{
if(y>sz){f[px]=(m/x)%p;return;}
for(int i=0; i<=k[y]; ++i,x*=pr[y])
dfs(x,y+1,z*(i+1),px+idx[y+1]*i);
}
void build()
{
auto vec=factorize(n);
int len=vec.size();
reverse(vec.begin(),vec.end());
for(int i=0; i<len; ++i)
{
int j=1;
while(i+1<len&&vec[i]==vec[i+1]) ++i,++j;
pr[++sz]=vec[i],k[sz]=j;
// printf("%lld %lld\n",pr[sz],k[sz]);
}
idx[sz+1]=1;
for(int i=sz; i>=1; --i)
idx[i]=idx[i+1]*(k[i]+1);
// cerr<<idx[1]<<endl;
dfs(1,1,1,0);
}
void calc(int v,int x,int y)
{
if(x>sz)
{
f[v]=(f[v]+p-f[v+idx[y+1]])%p;
return ;
}
for(int i=0; i<=k[x]-(x==y); ++i) calc(v+idx[x+1]*i,x+1,y);
}
int cur[103];
void solve2(int val,int x,int y,int z)
{
if(z>sz)
{
if(x==y) return ;
f[x]=(f[x]+val*g[x-y])%p;
return ;
}
for(int i=cur[z]; i<=k[z]; ++i)
{
if(i>cur[z]) val=qp(val,pr[z]);
solve2(val,x+(i-cur[z])*idx[z+1],y,z+1);
}
}
void solve1(int x,int y,int px)
{
if(y>sz) return solve2(f[px],px,px,1);
for(int i=0; i<=k[y]; ++i,x*=pr[y])
cur[y]=i,solve1(x,y+1,px+i*idx[y+1]);
}
void solve2_(int val,int x,int y,int z)
{
if(z>sz)
{
if(x==y) return ;
g[x]=(g[x]+p-val)%p;
return ;
}
for(int i=cur[z]; i<=k[z]; ++i)
{
solve2_(val,x+(i-cur[z])*idx[z+1],y,z+1);
}
}
void solve1_(int x,int y,int px)
{
if(y>sz)
{
if(x==1) return ;
g[px]=(g[px]+1)%p;
return solve2_(g[px],px,px,1);
}
for(int i=0; i<=k[y]; ++i,x*=pr[y])
cur[y]=i,solve1_(x,y+1,px+i*idx[y+1]);
}
signed main()
{
if(n==1) printf("%lld\n",m%p),exit(0);
build();
for(int i=1; i<=sz; ++i) calc(0,1,i);
reverse(f,f+idx[1]);
// solve(1,1,1,0,0);
solve1_(1,1,0);
solve1(1,1,0);
printf("%lld\n",f[idx[1]-1]);
return 0;
}
詳細信息
Test #1:
score: 100
Accepted
time: 1ms
memory: 5808kb
input:
4 4
output:
6
result:
ok 1 number(s): "6"
Test #2:
score: 0
Accepted
time: 1ms
memory: 5804kb
input:
2338 1470
output:
18530141
result:
ok 1 number(s): "18530141"
Test #3:
score: 0
Accepted
time: 1136ms
memory: 6704kb
input:
941958815880242160 945059392259579928
output:
57894579
result:
ok 1 number(s): "57894579"
Test #4:
score: -100
Time Limit Exceeded
input:
876240758958364800 893076802030549616