Uva 10294 Polya

#include <bits/stdc++.h>

using namespace std;

typedef long long LL;

int gcd(int a,int b) {
    return b ==0 ? a : gcd(b,a%b);
}

const int maxn = 55;

int main()
{
    int t,n;
    while(scanf("%d%d",&n,&t)!=EOF) {
        LL pow[maxn];
        pow[0] = 1;
        for(int i=1;i<=n;i++)
            pow[i] = pow[i-1] * t;

        LL a = 0;
        for(int i=0;i<n;i++)
            a +=pow[gcd(i,n)];
        LL b = 0;
        if(n%2==1) b = n*pow[(n+1)/2];
        else b = n/2*pow[n/2] + n/2*pow[n/2+1];
        printf("%lld %lld\n",a/n,(a+b)/2/n);

    }

    return 0;
}