Extended Euclidean algorithms to solve Bezout's identity:
           a*x + b*y = gcd(x, y)
        Finds one particular solution for x, y: s, t
        Returns: gcd, s, t

def _extended_gcd(self, a, b):
        """
        Extended Euclidean algorithms to solve Bezout's identity:
           a*x + b*y = gcd(x, y)
        Finds one particular solution for x, y: s, t
        Returns: gcd, s, t
        """
        s, old_s = 0, 1
        t, old_t = 1, 0
        r, old_r = b, a
        while r:
            quotient = old_r // r
            old_r, r = r, old_r - quotient * r
            old_s, s = s, old_s - quotient * s
            old_t, t = t, old_t - quotient * t
        return old_r, old_s, old_t