# Arithmetics functions implementaton

def modpow(a: int, b: int, m: int) -> int:
    result = 1 
    while b > 0:
        if (b & 1) > 0:
            result = (result * a) % m
        b = b >> 1 
        a = (a * a) % m 
    return result

def gcd(a: int, b: int) -> int:
    if b == 0:
        return a
    return gcd(b, a % b)

def mod_inverse(A: int, M: int) -> int:
    m0 = M
    y = 0
    x = 1
    if (M == 1):
        return 0
    while (A > 1):
        # q is quotient
        q = A // M
        t = M
        # m is remainder now, process
        # same as Euclid's algo
        M = A % M
        A = t
        t = y
        # Update x and y
        y = x - q * y
        x = t
    # Make x positive
    if (x < 0):
        x = x + m0
    return x