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Bulgarian Contest September 2001

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C. Power

Time limit: 0.5 second
Memory limit: 64 MB
You are given the whole numbers N, M and Y. Write a program that will find all whole numbers X in the interval [0, M − 1] such that XN mod M = Y.

Input

The input contains a single line with N, M and Y (0 < N < 999, 1 < M < 999, 0 < Y < 999) separated with one space.

Output

Output all numbers X separated with space on one line. The numbers must be written in ascending order. If no such numbers exist then output −1.

Sample

inputoutput
2 6 4
2 4
Problem Source: Bulgarian National Olympiad Day #1
To submit the solution for this problem go to the Problem set: 1110. Power