POJ 1286 Necklace of Beads(项链的珠子)

/*Polya原理*/
#include <cstdio>
#include <iostream>
using namespace std;
long long aaaa(long long a,long long b)
{
    long long res=1,tmp=a;
    while(b) 
    {
        if (b&1) 
            res*=tmp;
        tmp*=tmp;
        b>>=1;
    }
    return res;
}
int gcd(int a,int b) 
{
    return b==0?a:gcd(b,a%b);
}
int main()
{
    int n;
    while ( ~scanf("%d", &n) && n != -1) 
    {
        long long a = 0, b = 0;
        for (int i=0;i<n;i++) 
        {
            a+=aaaa(3,gcd(i,n));
        } 
        if (n&1) 
            b=(long long)n*aaaa(3,(n+1)/2);
        else 
            b=(long long)n/2*(aaaa(3,n/2+1)+aaaa(3,n/2));
        if (n==0) 
            printf("0\n");
        else 
            printf("%lld\n",(a+b)/2/n);
    }
    return 0;
}