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: Wrong Answer)


from functools import lru_cache


@lru_cache(maxsize=None)
def gcd(a, b):
    if b == 0:
        return a
    return gcd(b, a % b)


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


def lcm_all(lst):
    curr = 1
    for l in lst:
        curr = lcm(curr, l)
    return curr


def submit():
    n, m = map(int, input().split())
    alist = list(map(int, input().split()))

    l = lcm_all(alist)
    x = l // 2
    if x > m:
        print(0)
    else:
        print(m // x // 2 + 1)


if __name__ == "__main__":
    submit()