def extendedEuclideanAlgorimth(a, b):
    """
    Compute the coefficients of the bezout's identity.

    Bezout's identity: for integer a and b exist integers x and y such that
        a * x + b * y = d, where d = gcd(a, b).

    Parameters
    ----------
    a: int
        One of the numbers used for compute the coefficients of the bezout's
        identity
    b: int
        One of the numbers used for compute the coefficients of the bezout's
        identity

    Returns
    -------
    out: tuple
        The coefficientes of the bezout's identity
    """
    r0, r1 = a, b
    s0, s1 = 1, 0
    t0, t1 = 0, 1

    while r1 != 0:
        quotient = r0 // r1
        r0, r1 = r1, r0 - quotient * r1
        s0, s1 = s1, s0 - quotient * s1
        t0, t1 = t1, t0 - quotient * t1

    return s0, t0