"""Extended Euclidean algorithm.

egcd(a, b) returns (g, x, y) such that a*x + b*y == g == gcd(a, b).
Works for negative inputs and zero.
"""

def egcd(a, b):
    if b == 0:
        if a < 0:
            return (-a, -1, 0)
        return (a, 1, 0)
    g, x1, y1 = egcd(b, a % b)
    q = a // b
    return (g, y1, x1 - q * y1)


def gcd(a, b):
    return egcd(a, b)[0]


def lcm(a, b):
    if a == 0 or b == 0:
        return 0
    return abs(a // gcd(a, b) * b)