"""
2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.
What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?
"""

import math
import random
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__} took {end_time - start_time:.6f} seconds")
        return result

    return wrapper


def is_probable_prime(n: int, trials: int = 10) -> bool:
    """Miller-Rabin素性测试（快速判断是否为质数）"""
    if n < 2:
        return False
    if n in (2, 3):
        return True
    if n % 2 == 0:
        return False

    # 将 n-1 写成 d * 2^s 的形式
    d = n - 1
    s = 0
    while d % 2 == 0:
        d //= 2
        s += 1

    # 测试
    for _ in range(trials):
        a = random.randrange(2, n - 1)
        x = pow(a, d, n)
        if x == 1 or x == n - 1:
            continue
        for _ in range(s - 1):
            x = pow(x, 2, n)
            if x == n - 1:
                break
        else:
            return False
    return True


def primes_up_to(n: int) -> list[int]:
    if n < 2:
        return []
    if n == 2:
        return [2]
    if n == 3:
        return [2, 3]

    primes = [2, 3]
    for i in range(5, n + 1, 2):
        if is_probable_prime(i):
            primes.append(i)

    return primes


@timer
def smallest_multiple(n: int) -> int:
    result = 1
    for p in primes_up_to(n):
        # 找出最大幂次
        exp = int(math.log(n, p))
        result *= p**exp
    return result


@timer
def python_solution(n: int) -> int:
    ls = list(range(1, n + 1))
    return math.lcm(*ls)


if __name__ == "__main__":
    print(smallest_multiple(20))
    print(python_solution(20))