### Description

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)

### 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".

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) .

### Sample Input

5 2 15 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

### Sample Output

01

3

2

0

3

1

2

0

no solution

no solution

1

9584351

462803587