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 <stdio.h>

typedef long long ll;

ll a[111111];

ll gcd(ll x, ll y) { return !y ? x : gcd(y, x % y); }
ll lcm(ll x, ll y) { return x / gcd(x, y) * y; }

int main(void)
{
	ll n, m, i, LCM = 1;

	scanf("%lld %lld", &n, &m);
	for (i = 0; i < n; i++)
	{
		scanf("%lld", &a[i]);
		a[i] /= 2;
		LCM = lcm(LCM, a[i]);

		if (LCM > m)
		{
			puts("0");
			return 0;
		}
	}

	for (i = 0; i < n; i++)
		if (!(LCM / a[i] % 2))
		{
			puts("0");
			return 0;
		}

	printf("%lld", m / LCM % 2 == 0 ? m / LCM / 2 : m / LCM / 2 + 1);
	return 0;
}