Modular Multiplicative Inverse

This page will find the Modular Multiplicative Inverse of two numbers (x-1 mod y, and: y-1 mod x); if they exists.
It finds them by using the Extended Euclidean Algorithm to solve the Bézout's identity.

Bézout's identity is: ax + by = gcd(a, b). [where x & y are the Multiplicative Inverse of a & b, respectively], if gcd(a, b) = 1.
We initially setup the following variables as: x = 1, y = 0, x' = 0, y' = 1.