# Discrete Logging

GivenaprimeP,2≤P <231,anintegerB,2≤B<P,and an integer N, 2 ≤ N < P, compute the discrete logarithm of N, base B, modulo P. That is, find an integer L such that BL == N(mod P) Input Read several lines of input, each containing P, B, N separated by a space. Output For each line print the logarithm on a separate line. If there are several, print the smallest; if there is none, print ``no solution''. Note: The solution to this problem requires a well known result in number theory that is probably expected of you for Putnam but not ACM competitions. It is Fermat’s theorem that states BP−1 == 1(mod P) for any prime P and some other (fairly rare) numbers known as base-B pseudoprimes. A rarer subset of the base-B pseudoprimes, known as Carmichael numbers, are pseudoprimes for every base between 2 and P − 1. A corollary to Fermat’s theorem is that for any m Sample Input 521 522 523 524 531 532 533 534 541 542 543 544 12345701 2 1111111 1111111121 65537 1111111111 B−m == BP−1−m(mod P)

2/2 Sample Output 0 1 3 2 0 3 1 2 0 no solution no solution 1 9584351 462803587