POJ 3641 Pseudoprime numbers （伪素数_快速幂）

Description

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

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

Output

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

Sample Input

3 210 3341 2341 31105 21105 30 0

Sample Output

nonoyesnoyesyes

#include<iostream>#include<cstdio>using namespace std;typedef long long ll;bool is_prime(int x){int i,j;for(i=2;i*i<=x;i++) if(x%i==0) return false;return true;}ll mod_pow(ll x,ll n,ll mod){ll res=1;while(n>0) {if(n&1) res=res*x%mod;x=x*x%mod;n>>=1;}return res;}int main(){int a,p,i,j;while(cin>>p>>a) {if(p==0 && a==0) break;if(is_prime(p)) {printf("no\n");continue;}if(mod_pow(a,p,p)==a) printf("yes\n");else printf("no\n");}return 0;}