CodeForces - 1228C Primes and Multiplication 數貢獻

題目鏈接：https://vjudge.net/problem/CodeForces-1228C

題解：把x的每個質因子找出來，計算n！對每個因子的貢獻

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll mod = 1e9 + 7;
const int N = 1e5 + 10;
int prime[N];
int ok[N], len;
vector<int> v;
ll x, n;
ll ksm(ll x, ll y) {
	ll res = 1;
	while(y) {
		if(y & 1) res = res * x % mod;
		x = x * x % mod;
		y >>= 1;
	}
	return res;
}
int main() {
	for(int i = 2; i <= 100000; i++) {
		if(!ok[i]) {
			prime[len++] = i;
		}
		for(int j = 0; j < len && (ll)prime[j] * i <= 100000; j++) {
			ok[i * prime[j]] = 1;
			if(i % prime[j] == 0) break;
		}
	}
	
	cin >> x >> n;
	for(int i = 0; i < len && (ll)prime[i] * prime[i] <= x; i++) {
		if(x % prime[i] == 0) {
			v.push_back(prime[i]);
			while(x % prime[i] == 0) x /= prime[i];
		}
	}
	if(x > 1) {
		v.push_back(x);
	}
	ll ans = 1;
	for(int i = 0; i < v.size(); i++) {
		ll cnt = v[i];
		ll num = 0;
		ll m = n;
		while(m) {
			num += m / cnt;
			m /= cnt;
		}
		ans = (ans * ksm(v[i], num)) % mod;
	}
	cout << ans << endl;
	return 0;
}