Pseudoprime numbers

Description

Fermat's theorem states that for any prime number p andfor any integer a > 1, a^p == a (mod p).That is, if we raise a to the pth power and divide byp, 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 asCarmichael Numbers, are base-a pseudoprimes for all a.)

Given 2 < p ≤ 1,000,000,000 and 1 < a <p, determine whether or not p is a base-apseudoprime.

Input contains several test cases followed by a line containing"0 0". Each test case consists of a line containing p anda. For each test case, output "yes" if p is a base-apseudoprime; otherwise output "no".

Input

Output

Sample Input

3 2 

10 3 

341 2 

341 3 

11052 

1105 3 

0 0

Sample Output

no 

no 

yes

no 

yes 

yes

1. #include<stdio.h>
2. #include<math.h>
3. int main()
4. {
5.    long longa,p;
6.    int isprime(longlong n);
7.    long longmodular(long longa,long longr,long longm);
8.    while(scanf("%lld%lld",&p,&a)!=EOF)
9.    {
10.       if(p==0&&a==0)
11.           break;
12.       long longresult;
13.       if(isprime(p))
14.           printf("no\n");
15.       else
16.       {
17.           if(a==modular(a,p,p))
18.   printf("yes\n");
19.           else
20.               printf("no\n");
21.       }
22.    }
23.    return 0;
24. }
25. int isprime(longlong n)
26. {
27.    if(n==2)
28.       return 1;
29.    if(n<=1||n%2==0)
30.       return 0;
31.    long longj=3;
32.    while(j<=(longlong)sqrt(double(n)))
33.    {
34.       if(n%j==0)
35.           return 0;
36.       j+=2;
37.    }
38.    return 1;
39. }
40. long long modular(longlong a,longlong r,longlong m)
41. {
42.    long longd=1,t=a;
43.    while(r>0)
44.    {
45.       if(r%2==1)
46.           d=(d*t)%m;
47.       r/=2;
48.       t=t*t%m;
49.    }
50.    return d;
51. } 
52.