---

def gf4_mul(x, y, R=0x3, MASK=0xF):
    z = 0
    v = x & MASK
    for i in range(4):
        if (y >> i) & 1:
            z ^= v
        msb = (v >> 3) & 1
        v = (v << 1) & MASK
        if msb:
            v ^= R
    return z & MASK

def gf4_inv(x):
    result = 1
    base = x
    exp = (1 << 4) - 2  # 14
    while exp:
        if exp & 1:
            result = gf4_mul(result, base)
        base = gf4_mul(base, base)
        exp >>= 1
    return result

for t in [1, 2, 3, 4, 5, 6, 7]:
    inv_t = gf4_inv(t)
    p = gf4_mul(t, inv_t)
    print(f"inv({t}) = {inv_t}, {t} * inv = {p} {'OK' if p == 1 else 'FAIL'}")