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 (2.4.0) (judge verdict: Wrong Answer)

N,M = map(int,input().split())
A = list(map(int,input().split()))
 
def how_two(n):
    a = 0
    while n %2 ==0:
        a+=1
        n//=2
    return a
 
log2 = how_two(A[0])
for i in A:
    tmplog2 = how_two(i)
    if log2!=tmplog2:
        log2 =0
        break
        
        
if log2==0:
    print(0)
else:
    from fractions import gcd
    l = 1
    for i in A:
        l = (l*i)//gcd(l,i)
        if l//2 >= 10**9:
            l = float('inf')
            break
    l //= 2
    ans = (M+l)//(2*l)
    
    print(ans)