hdu 4059 The Boss on Mars 容斥原理

#include<iostream>
#include<stdio.h>
#include<algorithm>
#include<iomanip>
#include<cmath>
#include<cstring>
#include<vector>
#define ll long long
#define pi acos(-1.0)
#define MAX 1000001
#define mod 1000000007
using namespace std;
ll prime[MAX],cnt,fac[MAX],num,n;
ll ans1,res,inv;
bool f[MAX];
void init()
{
ll i,j;
cnt=0;
for(i=2;i<MAX;i++){
if(f[i]==0){
prime[cnt++]=i;
for(j=i*i;j<MAX;j+=i)
f[j]=1;
}
}
}
ll pows(ll a,ll b)
{
ll ans=1;
while(b){
if(b&1) ans=ans*a%mod;
b>>=1;
a=a*a%mod;
}
return ans%mod;
}
ll cal(ll m)
{
ll ans=(((6*pows(m,5)%mod+15*pows(m,4)%mod)%mod+10*pows(m,3)%mod)%mod-m+mod)%mod;
if(ans<0) ans=(ans%mod+ans)%mod;
ans=ans*inv%mod;
return ans;
}
void factor(ll m)
{
num=0;
for(int i=0;i<cnt&&prime[i]*prime[i]<=m;i++){
if(m%prime[i]==0){
fac[num++]=prime[i];
m/=prime[i];
while(m%prime[i]==0){
m/=prime[i];
}
}
}
if(m>1) fac[num++]=m;
}
void dfs(ll a,int m,int c)
{
if(a>=n) return ;
ll t=(ll)(n-1)/a;
ans1=(ans1+c*pows(a,4)%mod*cal(t)%mod)%mod;
if(ans1<0) ans1=(ans1%mod+mod)%mod;
for(int i=m+1;i<num;i++)
dfs((ll)a*fac[i],i,-c);
}
int main(){
int t;
init();
scanf("%d",&t);
inv=pows(30,mod-2);
while(t--){
scanf("%lld",&n);
if(n==1){
printf("1\n");
continue;
}
factor(n);
ans1=0;
for(int i=0;i<num;i++)
dfs(fac[i],i,1);
res=cal(n-1);
res-=ans1;
while(res<0) res=(res%mod+mod)%mod;
printf("%lld\n",res);
}
return 0;
}