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: Runtime Error)

import copy

def main():
    def gcd(a, b):
        if b == 0:
            return a
        else:
            return gcd(b, a%b)

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

    n, m = map(int, input().split())
    # これだと72がREになる
    A = set([int(x) for x in input().split()])
    # これだと74も78もREになる
    # A = [int(x) for x in input().split()]
    A_ = copy.deepcopy(A)
    a_lcm = A.pop()
    # Aの要素が複数ならlcmを計算する
    if len(A) >= 1:
        for a in A:
            a_lcm = lcm(a_lcm, a)
    else:
        a_lcm = a_lcm
    # 元のAの値とlcmの半分の値を割り切れるものがあったら0
    for i in A_:
        if (a_lcm / 2) % i == 0:
            print(0)
            exit()
        else:
            continue
    # mがlcmの半分よりも小さかったら0
    if a_lcm / 2 > m:
        print(0)
    else:
        # あとは定数倍の数調べて終わり
        # ans = int((m - (a_lcm / 2))) // a_lcm + 1
        ans = int((m - (a_lcm / 2)) // a_lcm) + 1
        print(ans)

if __name__ == '__main__':
    main()