题目描述

Given a prime $P$, an integer $B$, and an integer $N$, compute the discrete logarithm of $N$, base $B$, modulo $P$. That is, find an integer $L$ such that

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

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 $m$

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

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

数据规模与约定

• For $100\%$ of Data, $2 \leq P < 2^{31}$, $2 \leq B < P$, $2 \leq N < P$.