# Discrete Logging

时间限制：1s 空间限制：128MB

### 题目描述

Given a prime P, 2 <= P < 2^{31}, an integer B, 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

` B`^{L} == N (mod P)

### 输入格式

Read several lines of input, each containing P,B,N separated by a space,

### 输出格式

for each line print the logarithm on a separate line. If there are several, print the smallest; if there is none, print "no solution".

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

` B`^{(P-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

` B`^{(-m)} == B^{(P-1-m)} (mod P) .

### 样例输入

5 2 1 5 2 2 5 2 3 5 2 4 5 3 1 5 3 2 5 3 3 5 3 4 5 4 1 5 4 2 5 4 3 5 4 4 12345701 2 1111111 1111111121 65537 1111111111

### 样例输出

0 1 3 2 0 3 1 2 0 no solution no solution 1 9584351 462803587

### 提示

没有写明提示

### 题目来源

没有写明来源