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;
typedef long long ll;

#define REP(i,n) for(ll i=0; i<ll(n); i++)
#define FOR(i,m,n) for(int i=int(m); i<int(n); i++)
#define ALL(obj) (obj).begin(),(obj).end()

const int  INF = 1 << 29;
const ll INFL = 1LL << 60;
const ll mod = 1000000007;


ll gcd(ll x, ll y) {
	if (y == 0) return x;
	return gcd(y, x%y);
}


int main() {
	ll n, m;
	cin >> n >> m;
	vector<ll> a(n);
	REP(i, n)cin >> a[i];
	REP(i, n)a[i] /= 2;

	ll d = 1;
	REP(i, n) {
		d = d * a[i] / gcd(d, a[i]);
		if (d > m) {
			cout << 0 << endl;
			return 0;
		}
	}

	ll e = m / d;

	e = (e + 1) / 2;

	cout << e << endl;

}