#include<iostream>

#include<cstdio>

#include<cstring>

using namespace std;

int const maxn=1e6+;

int X,n,p,pri[maxn],cnt,ans;

bool vis[maxn];

int phi(int n)

{

    int ret=n;

    for(int i=;i*i<=n;i++)

    {

        if(n%i)continue;

//        (ret-=ret/i)%=p;// 有除法，不可随时取模

        ret-=ret/i;

        while(n%i==)n/=i;

    }

//    if(n!=1)(ret-=ret/n)%=p;// 有除法，不可随时取模

    if(n!=)ret-=ret/n;

    return ret%p;

}

int pw(int a,int b)

{

    int ret=; a%=p;//!!!

    for(;b;b>>=,(a*=a)%=p)

        if(b&)(ret*=a)%=p;

    return ret;

}

int main()

{

    scanf("%d",&X);

    while(X--)

    {

        scanf("%d%d",&n,&p);

        ans=;

        for(int i=;i*i<=n;i++)

        {

            if(n%i)continue;

            (ans+=phi(n/i)*pw(n,i-))%=p;

            if(i*i!=n)(ans+=phi(i)*pw(n,n/i-))%=p;

        }

        printf("%d\n",ans);

    }

}