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)

from math import gcd, ceil


def prime_factor(n):
    res = []
    for i in range(2, int(n ** 0.5) + 1):
        while n % i == 0:
            res.append(i)
            n //= i
    if n > 1:
        res.append(n)
    return res


if __name__ == "__main__":
    n, m = map(int, input().split())
    a = list(map(int, input().split()))
    twos_cnt = {prime_factor(num).count(2) for num in a}
    if len(twos_cnt) > 1:
        print(0)
        exit()

    num_two = twos_cnt.pop()
    a_div = [x >> num_two for x in a]

    a_div_lcm = a_div[0]
    for i in range(1, n):
        a_div_lcm = a_div_lcm * a_div[i] // gcd(a_div_lcm, a_div[i])
    print(ceil(m / a_div_lcm * 0.5 - 0.5))