"""
An irrational decimal fraction is created by concatenating the positive integers:
    0.123456789101112131415161718192021...

It can be seen that the 12th digit of the fractional part is 1.

If d_n represents the nth digit of the fractional part, find the value of the following expression.

    d_1 × d_10 × d_100 × d_1000 × d_10000 × d_100000 × d_1000000
"""

import time

def timer(func):
    def wrapper(*args, **kwargs):
        start_time = time.time()
        result = func(*args, **kwargs)
        end_time = time.time()
        print(f"{func.__name__} time: {end_time - start_time:.6f} seconds")
        return result
    return wrapper

class ChampernownesConstant:
    def __init__(self):
        self._cache = "123456789"
        self._level = 1
        self._nth = 1

    def __iter__(self):
        if self._nth > len(self._cache):
            self._level += 1
            self._cache += "".join(str(i) for i in range(10**(self._level-1), 10**self._level))
        yield self._cache[self._nth-1]
        self._nth += 1

    def __next__(self):
        return next(self.__iter__())

    def get_nth_digit(self, nth:int) -> int :
        while True:
            if nth > len(self._cache):
                self._level += 1
                self._cache += "".join(str(i) for i in range(10**(self._level-1), 10**self._level))
            else:
                return int(self._cache[nth-1])


@timer
def main_longstring() -> None:
    gen = ChampernownesConstant()
    ziel = [1,10,100,1000,10000,100000,1000000]
    res = 1
    for i in ziel:
        res *= gen.get_nth_digit(i)
    print(res)


def length_numbers(k:int) -> int :
    """计算前k位数的总位数"""
    if k == 0:
        return 0
    return (10**k * (9*k - 1) + 1) // 9


def get_nth_digit(nth:int) -> int :
    if nth < 0 :
        raise ValueError("nth must be non-negative")
    level = 1
    while length_numbers(level) < nth :
        level += 1
    # 计算在k位数中的偏移量
    offset = nth - length_numbers(level-1) # 在k位数中的第几个数字
    num_index = (offset - 1) // level      # 第几个k位数（从0开始）
    num = 10**(level-1) + num_index        # 具体的数字
    digit_index = (offset - 1) % level     # 在数字中的位置

    return int(str(num)[digit_index])


@timer
def main_quick() -> None :
    ziel = [1,10,100,1000,10000,100000,1000000]
    res = 1
    for i in ziel:
        res *= get_nth_digit(i)
    print(res)


if __name__ == "__main__":
    main_longstring()
    main_quick()