import math

nums = [
    [2, 1],
    [3, 2],
    [4, 1],
    [5, 4],
    [6, 5],
    [7, 4],
    [8, 1],
    [9, 2],
    [10, 9],
    [11, 0],
    [12, 5],
    [13, 10],
    [14, 11],
    [15, 14],
    [16, 9],
    [17, 0],
    [18, 11],
    [19, 18],
    [20, 9],
    [21, 11],
    [22, 11],
    [23, 15],
    [24, 17],
    [25, 9],
    [26, 23],
    [27, 20],
    [28, 25],
    [29, 16],
    [30, 29],
    [31, 27],
    [32, 25],
    [33, 11],
    [34, 17],
    [35, 4],
    [36, 29],
    [37, 22],
    [38, 37],
    [39, 23],
    [40, 9],
    [41, 1],
    [42, 11],
    [43, 11],
    [44, 33],
    [45, 29],
    [46, 15],
    [47, 5],
    [48, 41],
    [49, 46],
]


def check(number):
    for num, mod in nums:
        a, b = divmod(number, num)
        if b != mod:
            print(f"{number} % {num} == {number % num} != {mod}")
            return False

    print(f"{number}: pass.")
    return True


def lcm(a, b):
    return a * b // math.gcd(a, b)


def cal_prime_nums(n):
    prime = [1] * (n + 1)
    prime[0] = prime[1] = 0
    for i in range(2, n + 1):
        j = i * i
        while j <= n:
            prime[j] = 0
            j += i

    res = []
    for idx, num in enumerate(prime):
        if num:
            res.append(idx)

    return res


ans = 2022040920220409
check(ans)

prime = cal_prime_nums(99)
ans = 1
product = 1
for num, mod in nums:
    while ans % num != mod:
        ans += product

    product = lcm(product, num)
    print(f"{ans} % {num} == {mod}")

print(ans)
check(ans)