Problem:
Score : 400 points

Problem Statement

Given are a sequence A= {a_1,a_2,......a_N} of N positive even numbers, and an integer M.

Let a semi-common multiple of A be a positive integer X that satisfies the following condition for every k (1 \leq k \leq N):

There exists a non-negative integer p such that X= a_k \times (p+0.5).

Find the number of semi-common multiples of A among the integers between 1 and M (inclusive).

Constraints

1 \leq N \leq 10^5

1 \leq M \leq 10^9

2 \leq a_i \leq 10^9

a_i is an even number.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
a_1 a_2 ... a_N

Output

Print the number of semi-common multiples of A among the integers between 1 and M (inclusive).

Sample Input 1

2 50
6 10

Sample Output 1

2

15 = 6 \times 2.5

15 = 10 \times 1.5

45 = 6 \times 7.5

45 = 10 \times 4.5

Thus, 15 and 45 are semi-common multiples of A. There are no other semi-common multiples of A between 1 and 50, so the answer is 2.

Sample Input 2

3 100
14 22 40

Sample Output 2

0

The answer can be 0.

Sample Input 3

5 1000000000
6 6 2 6 2

Sample Output 3

166666667

Solution in Python (3.8.2) (judge verdict: Accepted)

# import sys
# sys.setrecursionlimit(10 ** 6)
# import bisect
# from collections import deque
def lcm(a, b):
    """最小公倍数"""
    from math import gcd
    return (a * b) // gcd(a, b)


# from decorator import stop_watch
#
#
# @stop_watch
def solve(N, M, As):
    if sum([a % 2 for a in As]) > 0:
        print(0)
        return

    As = [a // 2 for a in As]
    all_lcm = 1
    for a in As:
        all_lcm = lcm(all_lcm, a)
        if all_lcm > M:
            print(0)
            return

    for a in As:
        if (all_lcm // a) % 2 == 0:
            print(0)
            return
    from math import ceil
    print(ceil(M // all_lcm / 2))


if __name__ == '__main__':
    N, M = map(int, input().split())
    As = [int(i) for i in input().split()]

    # import random
    # N, M = 10 ** 5, 10 ** 9
    # As = [random.randint(5, 5) * 2 for _ in range(N)]
    solve(N, M, As)