[BZOJ 3884]上帝與集合的正確用法：歐拉定理

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題解見出題人blog http://blog.csdn.net/popoqqq/article/details/43951401

/*
User:Small
Language:C++
Problem No.:3884
*/
#include<bits/stdc++.h>
#define ll long long
#define inf 999999999
using namespace std;
int phi(int n){
    int res=n;
    for(int i=2;i*i<=n;i++){
        if(n%i==0){
            res=res/i*(i-1);
            while(n%i==0) n/=i;
        }
    }
    if(n!=1) res=res/n*(n-1);
    return res;
}
int pow(int a,int b,int p){
    int res=1;
    while(b){
        if(b&1) res=(ll)res*a%p;
        a=(ll)a*a%p;
        b>>=1;
    }
    return res;
}
int solve(int p){//solve(p)計算的是無限個2 mod p的值 
    if(p==1) return 0;
    int tmp=0;
    while((p&1)==0) p>>=1,tmp++;
    int phi_p=phi(p);
    int res=solve(phi_p);
    res=(res+phi_p-tmp%phi_p)%phi_p;
    res=pow(2,res,p)%p;
    return res<<tmp;
}
int main(){
    freopen("data.in","r",stdin);//
    int t;
    scanf("%d",&t);
    while(t--){
        int p;
        scanf("%d",&p);
        printf("%d\n",solve(p));
    }
    return 0;
}