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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
    static long gcd(long a, long b) 
    { 
    if (a == 0) 
        return b;  
    return gcd(b % a, a);  
    } 
  
    static long lcm(long a, long b) 
    { 
        return (a*b)/gcd(a, b); 
    } 
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		Scanner s=new Scanner(System.in);
		int n=s.nextInt();
		long k=s.nextLong();
		long a[]=new long[n];
		for(int i=0;i<n;i++)
		a[i]=s.nextLong();
		HashSet<Long>hs1=new HashSet<Long>();
		for(int i=0;i<n;i++)
		hs1.add(a[i]/2);
		Iterator<Long>it=hs1.iterator();
		long kk=1;
		while(it.hasNext())
		{kk=lcm(kk,it.next());}
		if(kk>k)
		System.out.println("0");
		else
		{long count=0;
		    long pp=k/kk;
		    if(pp%2==0)
		    count=pp/2;
		    else
		    count=pp/2+1;
		System.out.println(count);}}}