poj3641

Pseudoprime numbers

Time Limit: 1000MS Memory Limit: 65536KTotal Submissions: 8075 Accepted: 3364

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

3 210 3341 2341 31105 21105 30 0

Sample Output

nonoyesnoyesyes

#include<iostream>#include<cmath>//#define LL long longtypedef long long LL;using namespace std;int prime(LL x){      if(x==2){return 1;}      if(x<=1 || x%2==0){return 0;}      LL j=3;      while(j<=(LL)sqrt(double(x))){               if(x%j==0){return 0;}               j=j+2;              }      return 1;    }    LL modular(LL a, LL r, LL m){            LL d=1,t=a;            while(r>0){                if(r%2==1){d=d*t%m;}                 r=r/2;                 t=t*t%m;                    }          return d;                 }                            int main(){    LL p,a;    while(/*cin>>p>>a*/scanf("%I64d%I64d",&p,&a)){     if(p==0&&a==0){break;}     if(prime(p)==1){printf("no\n");}     else{     if(modular(a,p,p)==a){printf("yes\n");}else{printf("no\n");}     }    }        return 0;    }