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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

import sys
read = sys.stdin.read
from math import gcd

def main():
    n, m, *a = map(int, read().split())
    if n == 1:
        r = m // (a[0]//2) + 1
        print(int(r))
        sys.exit()
    d = [0] * n
    for i, ae in enumerate(a):
        t1 = 0
        while ae > 0:
            if ae % 2 == 0:
                t1 += 1
                ae /= 2
            else:
                break
        d[i] = t1
    d_c = [de == d[0] for de in d]
    if not all(d_c):
        print(0)
        sys.exit()

    div = 2**d[0]
    a2 = [ae // div for ae in a]
    m /= div
    g = (a2[0] * a2[1]) // gcd(a2[0], a2[1])
    for i1 in range(1, n):
        g = (g * a2[i1]) // gcd(g, a2[i1])
        if g > m:
            print(0)
            sys.exit()

    r = m // g + 1
    print(int(r))

if __name__ == '__main__':
    main()