ACM-ICPC 2018 沈阳赛区网络预赛 G Spare Tire (素因子分解+容斥）

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样例输入复制

4 4

样例输出复制

14

#include<bits/stdc++.h>
using namespace std;

typedef long long ll;
const ll MOD=1e9+7,inv2=500000004,inv6=166666668;
ll n,m;
const int maxn=100000;
ll A(ll x) {
	x %= MOD;
	return ((x * x) + x) % MOD;
}

ll mul(ll a, ll b) {
	a %= MOD, b %= MOD;
	return (a *b) % MOD;
}

ll kA(ll t,ll k) {
	ll res= (t+k*t)%MOD;
	res = (res*k)%MOD;
	res = (res*inv2)%MOD;
	ll h = (mul(mul(k,k+1),2*k+1)*inv6)%MOD;
	h = (h*t)%MOD;
	h = (h*t)%MOD;
	res = (res+h)%MOD;
	return res;
}

ll a[maxn];
ll b[maxn];

void factor(ll n,ll &tot) {
	ll temp,i,now;
	temp=(ll)((double)sqrt(n)+1);
	tot=0;
	now=n;
	for(i=2; i<=temp; ++i)if(now%i==0) {
			a[++tot]=i;
			b[tot]=0;
			while(now%i==0) {
				++b[tot];
				now/=i;
			}
		}
	if(now!=1) {
		a[++tot]=now;
		b[tot]=1;
	}
}

int main() {
	while(scanf("%d%d",&n,&m)!=EOF) {
		ll all;
		factor(m,all);
		ll g=0;
		for(int i=1; i<(1<<all); i++) {
			int cnt=0,t=1;
			for(int j=0; j<all; j++) {
				if((i>>j)&1) {
					t*=a[j+1];
					cnt++;
				}
			}
			if(cnt&1) {
				if(n/t==0||t>n) continue;
				g = (g+kA(t,n/t))%MOD;
			} else {
				if(n/t==0||t>n) continue;
				g = (g-kA(t,n/t)+MOD)%MOD;
			}
		}
		ll ans=g;
		ll other = (mul(n, n + 1)*inv2 + mul(mul(n,n+1),2*n+1)*inv6)%MOD;
		ans = (other - ans + MOD)% MOD;
		cout<<ans<<endl;
	}
	return 0;
}