import random
from mod_inverse import modinv

def test_basic():
    assert modinv(3, 11) == 4
    assert modinv(10, 17) == 12
    assert modinv(1, 5) == 1

def test_none():
    assert modinv(2, 4) is None
    assert modinv(6, 9) is None
    assert modinv(0, 5) is None

def test_negative_a():
    assert modinv(-1, 7) == 6
    assert ( (-1)*modinv(-1,7) ) % 7 == 1 % 7

def test_brute():
    for m in range(2, 200):
        for a in range(0, m):
            x = modinv(a, m)
            g = None
            # compute gcd
            import math
            if math.gcd(a % m, m) != 1:
                assert x is None, (a, m, x)
            else:
                assert x is not None and 0 <= x < m
                assert (a * x) % m == 1

def test_random_large():
    random.seed(1)
    for _ in range(2000):
        m = random.randint(2, 10**6)
        a = random.randint(0, m-1)
        x = modinv(a, m)
        import math
        if math.gcd(a, m) != 1:
            assert x is None
        else:
            assert x is not None and (a*x)%m == 1

if __name__ == "__main__":
    test_basic(); test_none(); test_negative_a(); test_brute(); test_random_large()
    print("ALL PASS")