Fermat's theorem states that for any prime number p and for any integer a > 1, a^p = a (mod p). That is, if we raise a to the p^th power and divide by p, the remainder is a. Some (but not very many) non-prime values of p, known as base-a pseudoprimes, have this property for some a. (And some, known as Carmichael Numbers, are base-a pseudoprimes for all a.)

Given 2 < p ≤ 1000000000 and 1 < a < p, determine whether or not p is a base-a pseudoprime.

Input contains several test cases followed by a line containing "0 0". Each test case consists of a line containing p and a.

For each test case, output "yes" if p is a base-a pseudoprime; otherwise output "no".

#include <iostream>

using namespace std;

typedef unsigned long long ull;

ull a,p;

bool testPrime(ull x)

{

    for(ull i=;i*i<=x;i++)

    {

        if(x%i==)

        {

            return false;

        }

    }

    return true;

}

ull mpow(ull x,ull n,ull mod)

{

    ull res=;

    while(n>)

    {

        if(n&)

        {

            res=(res*x)%mod;

        }

        x=(x*x)%mod;

        n>>=;

    }

    return res;

}

int main()

{

    while(cin>>p>>a)

    {

        if(a==&&p==)    break;

        if(testPrime(p))

        {

            cout<<"no"<<endl;

        }

        else

        {

            if(mpow(a,p,p)==a%p)

            {

                cout<<"yes"<<endl;

            }

            else

            {

                cout<<"no"<<endl;

            }

        }

    }

    return ;

}