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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

# include <bits/stdc++.h>
using namespace std;
long long n,m,a[1000005],a1[1000005],v2[1000005],usj,k,m1;
map <long long, long long> ans1;
int main()
{
	cin>>n>>m;
	for (int i=1; i<=n; i++)
	{
		cin>>a[i];
		a[i]/=2;
	}
  long long usg=a[1];
  long long usj=a[1];
	for (int i=2 ; i<=n; i++)
    {
      usg=__gcd(usj,a[i]);
      usj=(usj*a[i])/usg;
      if (usj>m) 
      {cout<<0<<endl;
       return 0;
      }
    }
       
          // cout<<usj<<endl;
 
 
	for (long long i=1; i<=n; i++)
	{
		if ((usj/a[i])%2==0)
		{
			cout<<0<<endl;
			return 0;
		}
	}
//  cout<<usj<<endl;
	k=m/usj;
	if (k%2==0) k/=2;
	else k=k/2+1;
	cout<<k<<endl;
}