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: Runtime Error)

def gcd(a, b):
    a, b = max([a, b]), min([a, b])
    if b == 0:
        return a
    else:
        return gcd(b, a % b)


def gcd_from_list(num_list):
    if len(num_list) == 1:
        return num_list[0]
    else:
        return gcd(num_list[0], gcd_from_list(num_list[1:]))


def lcm_from_list(num_list):
    gcd_of_input = gcd_from_list(num_list)
    num_list = list(set(num_list))
    lcm = num_list[0]
    for i in range(len(num_list) - 1):
        lcm = lcm * num_list[i + 1] // gcd_of_input
    return lcm


def main():
    N, M = list(map(int, input().split(' ')))
    half_A = list(map(lambda x: int(x) // 2, input().split(' ')))
    lcm_A = lcm_from_list(half_A)
    num_multiples = M // lcm_A
    print((num_multiples + 1) // 2)  # count only cases that ratios are odd numbers.


if __name__ == '__main__':
    main()