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 (3.4.3) (judge verdict: Accepted)

import sys

read = sys.stdin.read
readline = sys.stdin.readline
readlines = sys.stdin.readlines
sys.setrecursionlimit(10 ** 9)
INF = 1 << 60


def gcd(a, b):
    while b:
        a, b = b, a % b
    return a


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


def main():
    N, M = map(int, input().split())
    A = list(set(map(int, input().split(" "))))
    B = A.copy()

    while not any(b % 2 for b in B):
        B = [b // 2 for b in B]

    if not all(b % 2 for b in B):
        print(0)
        return

    semi_lcm = 1
    for a in A:
        semi_lcm = lcm(semi_lcm, a // 2)

    print((M // semi_lcm + 1) // 2)
    return


if __name__ == '__main__':
    main()