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)

def gcd(a, b):
    if b > a:
        a, b = b, a
    while b > 0:
        a, b = b, a % b        
    return a


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


def get_t(n):
    t = 0
    while n % 2 == 0:
        n //= 2
        t += 1
    return t


def main():
    n, m = map(int, input().split())
    a = [int(i) // 2 for i in input().split()]
    
    t = get_t(a[0])
    l = a[0] // 2**t
    m //= 2**t
    for i in range(1, len(a)):
        count = get_t(a[i])
        if count != t:
            return 0         

        l = lcm(a[i] // 2**t, l)
        if l > m:
            return 0
    
    m //= l
    ans = (m + 1) // 2
    
    return ans       
   

if __name__ == '__main__':
    ans = main()
    print(ans)