from math import floor
from time import time_ns


def d(_num: int, den: int, n: int) -> int:
    """ (10^n // d) % 10 -> (10^n % 10*d) // d % 10 """
    return pow(10, n, 10 * den) // den % 10


def d_naiv(num: int, den: int, n: int, debug: bool = False) -> int:
    """Return the nth digit of the factional part of num / den."""
    if num == den:
        if debug:
            print("1.0")
        return 0
    assert num < den
    if debug:
        print("0.", end="")

    x = None
    r = 0
    i = 0
    num *= 10  # 0.
    nums = {}
    while i < n:
        if num == 0:
            r = 0
            break
        elif num < den:
            r = 0
            if debug:
                print(0, end="")
        else:
            r = num // den
            num %= den
            if debug:
                print(r, end="")
        i += 1
        if x is None:
            if num in nums:
                j = nums[num]
                delta = i - j
                x = floor((n - i) / delta)
                if debug:
                    print("---")
                    print(f"{den=} {j} -> {i} (d={delta} mult={x})")
                    print(f"\n{j} -{delta} {x}> {i} ")
                i += x * delta
            else:
                nums[num] = i
        num *= 10
    if debug:
        print()
    # dr = (10**n % (10*den)) // den
    dr = pow(10, n, 10 * den) // den
    assert r == dr
    # print(f"k = {den} n= {n}")
    return r


def s(n: int) -> int:
    return sum(d(1, k, n) for k in range(1, n + 1))


def euler_820():
    d(1, 7, 10)
    assert d(1, 2, 7) == 0
    assert d(1, 3, 7) == 3
    assert d(1, 5, 7) == 0
    assert d(1, 6, 7) == 6
    assert d(1, 7, 7) == 1
    assert s(7) == 10
    assert s(100) == 418
    assert s(10000) == 43742
    return s(10**7)


if __name__ == "__main__":
    solution = euler_820()
    print(f"e820.py: {solution}")
    assert solution == 44967734