Problem F

Inverse Affine Transform

Input File: pf.in

Time Limit: 3 seconds

        Let m be a positive integer, under a modular arithmetic, an affine transform
on the set S = {0,1,2,…,m-1} can be defined as

                                                y ≡ ax+b  mod  m                               (1)

Some permutations on an integer set S could be implemented based on the
above affine transform with parameters a and m being relatively prime, that
is, their greatest common divisor gcd(a,m) = 1. If gcd(a, m) = 1, the inverse
transform exists which is also an affine transform, say,

                                                x ≡ cy+d  mod  m                               (2)

        This problem asks you to write a program to dectect and compute the
inverse transform of an affine transform with the given parameters m, a, b.