Returns the last nonzero digits of a factorial

fact.py

"""
This code provides functions to find the last nonzero values of a positive factorial.
"""


def f(n: int, k: int) -> int:
    """
    Returns the k last nonzero digits.
    .. note::
        As f(10**100, 13) is a Googolbang where the 13 last nonzero
        digits are 5473738735616 with 25*(10**98)-18 trailing zeros.
    :long_url: https://www.wolframalpha.com/input?i=googol!
    """
    m, l = 10 ** k, [1, 1]
    for i in range(2, m):
        if i % 2 == 0 or i % 5 == 0: i = 1
        l.append((l[-1] * i) % m)

    def nf(j: int) -> int:
        a, b = divmod(j, m)
        return (pow(l[m - 1], a, m) * l[b]) % m

    ans, p = 1, 1
    while p <= n:
        q = p
        while q <= n:
            ans = (ans * nf(n // q)) % m; q *= 5
        p *= 2

    def legendre(n: int, p: int) -> int:
        """
        Should be moderate if there are zeros inside the last nonzero digits calculation of Legendre's formula.
        """
        ans = 0
        while n:
            n //= p; ans += n
        return ans

    ans *= pow(2, legendre(n, 2) - legendre(n, 5), m)
    return ans % m


if __name__ == "__main__":
    try:
        print(f(int(abs(float(__import__("sys").argv[1]))), int(abs(float(__import__("sys").argv[2])))))
    except (IndexError, MemoryError, TypeError, ValueError) as e:
        print(e)