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def euclidGCD(a, b):  # sourcery skip: assign-if-exp, reintroduce-else
    if a < 0 or b < 0:
        return None
    if a < b:
        return euclidGCD(b, a)
    if a % b == 0:
        print(f"{a} = {b} * {a//b} + {a%b}")
        return b
    print(f"{a} = {b} * {a//b} + {a%b}")
    return euclidGCD(b, a % b)

x, y = 0, 1
def extEuclidGCD(a, b):
    global x, y
    if (a == 0):
        x, y = 0, 1
        return b
 
    gcd = extEuclidGCD(b % a, a)
    x1, y1 = x, y

    x, y = y1 - (b // a) * x1, x1
    return gcd

def moduloInverse(a, b):  # sourcery skip: assign-if-exp
    gcd = extEuclidGCD(a, b)
    if gcd != 1:
        return None
    else:
        return (x % b + b) % b

while True:
    a = input("Enter the first number: ")
    b = input("Enter the second number: ")
    try:
        a = int(a)
        b = int(b)
        break
    except ValueError:
        print("Invalid input. Try again.")

print(f"GCD: {euclidGCD(a, b)}")
print(f"GCD using extended: {extEuclidGCD(a, b)}")
print(f"Modular multiplicative inverse is: {moduloInverse(a, b)} ")