POJ 2154 Color

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#define maxn 100050
using namespace std;
int t,n,mod,prime[maxn],tot=0;
bool vis[maxn];
void get_table()
{
    for (int i=2;i<=maxn-50;i++)
    {
        if (!vis[i]) prime[++tot]=i;
        for (int j=1;j<=tot && i*prime[j]<=maxn-50;j++)
        {
            vis[i*prime[j]]=true;
            if (!i%prime[j]) break;
        }
    }
}
int f_pow(int a,int b)
{
    a%=mod;
    int base=a,ans=1;
    while (b)
    {
        if (b&1) ans=(ans*base)%mod;
        base=(base*base)%mod;
        b>>=1;
    }
    return ans;
}
int phi(int x)
{
    int ret1=1,ret2=1,top=x;
    for (int i=1;i<=tot && prime[i]*prime[i]<=top;i++)
    {
        if (x%prime[i]) continue;
        ret1*=(prime[i]-1);ret2*=prime[i];
        while (x%prime[i]==0) x/=prime[i];
    }
    if (x!=1) {ret1*=(x-1);ret2*=x;}
    double rr=(double)top/ret2*ret1;
    return (int)rr%mod;
}
void work()
{
    int top=sqrt(n),ans=0;
    for (int i=1;i<=top;i++)
    {
        if (n%i) continue;
        ans+=f_pow(n,i-1)*phi(n/i)%mod;ans%=mod;
        if ((i!=top) || (top*top!=n)) 
        {
            ans+=f_pow(n,n/i-1)*phi(i)%mod;
            ans%=mod;
        }
    }
    printf("%d\n",ans);
}
int main()
{
    scanf("%d",&t);
    get_table();
    for (int i=1;i<=t;i++)
    {
        scanf("%d%d",&n,&mod);
        work();
    }
    return 0;
}