Pseudoprime numbers

Fermat’s theorem states that for any prime numberpandforanyintegera>1,ap ==a (mod p). That is, if we raise a to the pth 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 ≤ 1, 000, 000, 000 and 1 < a < p, determine whether or not p is a base-a pseu- doprime. 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 32 10 3 341 2 341 3 1105 2 1105 3 00 Sample Output no no yes no yes yes