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)

from math import gcd
from functools import reduce
import sys
input = sys.stdin.readline


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


def count_factor_2(num):
    count = 0
    while num % 2 == 0:
        num //= 2
        count += 1
    return count


def main():
    n, m = map(int, input().split())
    A = list(map(lambda x: int(x)//2, input().split()))

    check = len(set(map(count_factor_2, A)))
    if check != 1:
        print(0)
        return

    lcm_a = reduce(lcm, A)
    step = lcm_a * 2
    ans = (m + lcm_a) // step
    print(ans)


if __name__ == "__main__":
    main()