Problem: 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).

Examples

Input

2 50
6 10


Output

2


Input

3 100
14 22 40


Output

0


Input

5 1000000000
6 6 2 6 2


Output

166666667

Solution (in CPP):

Solution:
#include <bits/stdc++.h>

using namespace std;

using ll = long long;
const ll MOD = 1e9 + 7;
const ll INF = 1e18;

ll gcd(ll x, ll y) {
    return y ? gcd(y, x%y) : x;
}

ll lcm(ll x, ll y) {
    return x * y / gcd(x, y);
}

int main() {
    ll n, m, i, j, k;
    cin >> n >> m;
    vector<ll> a(n);
    ll l = 1;
    for(auto &x : a) {
        cin >> x;
        l=lcm(l,x/2);
    }
    ll ret = 0;
    //cout << l << endl;
    for(auto &x:a){
        if(l%x==0){
            cout << 0 << endl;
            return 0;
        }
    }
    cout << (m/l+1)/2 << endl;
    return 0;
}