#!/usr/bin/env python3

def gcd(a, b):
    """
        This function calculate the GCD (Greatest Common Divisor of the number a of b
        Args:
            a (Integer): the number a
            b (integer): the number b

        Return:
            the GCD 
    """

    if b == 0:
        return a
    return gcd(b, a%b)

def egcd(a, b):
    """
        This function compute the Extended Euclidean algorithm
        https://user.eng.umd.edu/~danadach/Cryptography_20/ExtEuclAlg.pdf
        https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm

        Args:
            a (Integer): the number a
            b (Integer): the number b
    """
    if a == 0:
        return b, 0, 1
    gcd, x1, y1 = egcd(b % a, a)
    x = y1 - (b // a) * x1
    y = x1
    return gcd, x, y