POJ 2154 Color ——Burnside引理

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;

#define F(i,j,k) for (int i=j;i<=k;++i)
#define D(i,j,k) for (int i=j;i>=k;--i)
#define maxn 100005
#define inf 0x3f3f3f3f

int n,p,x,sum;
int ispr[maxn],pr[maxn],top=0;

void init()
{
	F(i,2,maxn-1)
		if (!ispr[i])
		{
			pr[++top]=i;
			F(j,2,inf)
			{
				if (j*i>=maxn) break;
				ispr[j*i]=1;
			}
		}
}

int qpow(int a,int b)
{
	a%=p;
	int ret=1;
	while (b)
	{
		if (b&1) (ret*=a)%=p;
		(a*=a)%=p;
		b>>=1;
	}
	return ret;
}

int phi(int n)
{
	int ret=n;
	for (int i=1;pr[i]*pr[i]<=n&&i<=top;++i)
		if (n%pr[i]==0)
		{
			ret=ret-ret/pr[i];
			while (n%pr[i]==0) n/=pr[i];
		}
	if (n>1) ret=ret-ret/n;
	return ret%p;
}

int main()
{
	init();
//	F(i,1,top) printf("%d ",pr[i]); printf("\n");
	scanf("%d",&x);
	while (x--)
	{
		sum=0;
		scanf("%d%d",&n,&p);
		for (int i=1;i*i<=n;++i)
		{
			if (n%i==0)
			{
				sum=(sum+(qpow(n,i-1)*phi(n/i))%p)%p;
				if (i*i!=n) sum=(sum+(qpow(n,n/i-1)*phi(i))%p)%p;
			}
		}
		printf("%d\n",sum);
	}
}