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>
#define rep(i, n) for (int i = 0; i < (n); i++)
#define all(x) (x).begin(), (x).end()
typedef long long ll;
using namespace std;

ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
ll lcm(ll a,ll b){return a/gcd(a,b)*b;}

int f(int x){
	int ans = 0;
	while(x%2 == 0){
		x /= 2;
		ans++;
	}
	return ans;
}

int main() {
    ll N, M;
    cin >> N >> M;
    vector<ll> A(N);
    rep(i, N) {
        int a;
        cin >> a;
        A[i] = a / 2;
    }

		int t = f(A[0]);
		rep(i,N){
			if(f(A[i]) != t){
				cout << 0 << endl;
				return 0;
			}
		}

		ll l = 1;
		rep(i,N){
			l = lcm(l,A[i]);
			if(l>M){
				cout << 0 << endl;
				return 0;
			}
		}
		cout << M/l - M/(2*l) << endl;
}