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.Arrays;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int N = sc.nextInt();
        int M = sc.nextInt();
        int[] A = new int[N];

        int minA = Integer.MAX_VALUE;

        for (int i = 0; i < N; i++) {
            A[i] = sc.nextInt();
            minA = Math.min(A[i], minA);
        }

        int count = 0;

        boolean[] checked = new boolean[M+1];
        Arrays.fill(checked, false);
        
        loop: for (int candidate = minA / 2; candidate <= M; candidate++) {
            if(checked[candidate]) {
                continue loop;
            }
            
            for (int a : A) {
                if ((2 * candidate) % a != 0) {
                    continue loop;
                }
                if (((2 * candidate) / a - 1) % 2 != 0) {
                    continue loop;
                }
            }
            
            for(int i=1;i * candidate <=M; i +=2) {
                checked[i*candidate] = true;
                count++;
            }

        }

        System.out.println(count);
    }

}