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: Runtime Error)

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];
   for(int i =0;i<N;i++) 
   {
     a[i] =sc.nextLong();
     a[i] /=2;
   }
   long tmp = a[0];
   for(int i =1;i<N;i++)
   {
     if(tmp%a[i]==0)
     {
       System.out.println(0);
       return;
     }
     tmp = lcm(tmp,a[i]);
   }
   long ans =0;
   if(M - tmp>=0)
   { 
     ans++;
     ans+= (M - tmp)/(2*tmp);
   }
   System.out.println(ans);
 }
  private static long lcm(long m, long n) {
    return m * n / gcd(m, n);
 }
  private static long gcd(long m, long n) {
    if(m < n) return gcd(n, m);
    if(n == 0) return m;
    return gcd(n, m % n);
 }
}