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.*;
import java.math.*;
public class Main{
	public static void main(String[] args){
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		long m=sc.nextLong();
		long l=1;
		int count2=0;
		for(int i=0; i<n; i++){
			long a =sc.nextLong();
			int tmp=0;
			while(a%2==0){
				a/=2;
				tmp++;
			}
			if(i==0){
				count2=tmp;
			}else if(count2!=tmp){
				System.out.println(00);
				return;
			}
			try{
			l=l*a/gcd(l,a);
			}catch(StackOverflowError e){
				System.out.println(00);
				return;
			}
		}
		long two=2;
		count2--;
		while(count2>0){
			if((count2 & 1)==1){
				l*=two;
			}
			two*=two;
			count2>>=1;
		}
		m/=l;
		System.out.println((m+1)/2);
	}
	private static long gcd(long m, long n) {
    if(m < n) return gcd(n, m);
		long tmp=m;
		while(n!=0){
			m=n;
			n=tmp%n;
		}
    return m;
}
}