POJ3641:Pseudoprime numbers

Description

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

Given 2 < p ≤ 1000000000 and 1 < a < p, determine whether or notp is a base-a pseudoprime.

Input

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

Output

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

Sample Input

3 2
10 3
341 2
341 3
1105 2
1105 3
0 0

Sample Output

no
no
yes
no
yes
yes

#include <iostream>
using namespace std;

int prime(long long a)
{
    int i;
    if(a == 2)
        return 1;
    for(i = 2; i*i<=a; i++)
        if(a%i == 0)
            return 0;
    return 1;
}

long long mod(long long a,long long b,long long m)
{
    long long ans = 1;
    while(b>0)
    {
        if(b&1)
        {
            ans = ans*a%m;
            //b--;
        }
        b>>=1;
        a = a*a%m;
    }
    return ans;
}

int main()
{
    long long a,p;

    while(cin >> p >> a && (p||a))
    {
        long long ans;
        if(prime(p))
        cout << "no" << endl;
        else
        {
            ans = mod(a,p,p);
            if(ans == a)
            cout << "yes" << endl;
            else
            cout << "no" << endl;
        }
    }

    return 0;
}