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 JAVA):

Solution:
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		long m = sc.nextLong();
		long[] a = new long[n + 1];
		long gcd = 0;
		long lcm = 1;
		for(int i = 0 ; i < n ; i++) {
			a[i] = sc.nextLong() / 2;
			gcd = gcd(lcm , a[i]);
			lcm = lcm * a[i] / gcd;
			if(lcm > m) {
				System.out.println(0);
				return;
			}
		}
		for(int i = 0 ; i < n ; i++) {
			if((lcm / a[i]) % 2 == 0) {
				System.out.println(0);
				return;
			}
		}

		sc.close();
		System.out.println((m / lcm + 1 ) / 2);

	}
	public static long gcd(long num1,long num2) {
        if(num2 == 0) return num1;
        else return gcd(num2 , num1 % num2 );
 }
}