from gmpy2 import mpz

def extended_gcd(a, b):
    if b == 0:
        return (a, mpz(1), mpz(0))
    else:
        gcd, x1, y1 = extended_gcd(b, a % b)
        x = y1
        y = x1 - (a // b) * y1
        return (gcd, x, y)

def modinv(b, n):
    gcd, x, y = extended_gcd(b, n)
    if gcd != 1:
        raise ValueError(f"Odwrotność modulo nie istnieje, ponieważ gcd({b}, {n}) = {gcd} ≠ 1.")
    else:
        return x % n

n = mpz(input("Podaj n: "))
b = mpz(input("Podaj b: "))

try:
    inverse = modinv(b, n)
    print(f"Odwrotność {b} modulo {n} to {inverse}.")
    if (b * inverse) % n == 1:
        print(f"Sprawdzenie: ({b} * {inverse}) mod {n} = 1\n")
    else:
        print("Błąd w obliczeniach.\n")
except ValueError as e:
    print(f"Dla b = {b}, n = {n}: {e}\n")