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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
using vec_int = vector<int>;
using P = pair<int,int>;
using T = tuple<int,int,int>;
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
using ll = long long;

ll Gcd(long m, long n)
{
	long temp;
	while (m % n != 0)
	{
		temp = n;
		n = m % n;
		m = temp;
	}
	return n;
}


int main(){
    ll N, M; cin>>N>>M;

    vector<int> A(N);
    rep(i,N){
        cin>>A.at(i);
    }

    ll temp = A.at(0);
    rep(i, N-1){
        temp = temp*A.at(i+1)/Gcd(temp, A.at(i+1));
    }

    ll aa = M-temp/2;
    cout << 1+int(aa/temp)<<endl;





 
}