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 C# (.NET Core 3.1.201) (judge verdict: Runtime Error)

using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Globalization;
using System.Linq;
using System.Runtime.InteropServices.ComTypes;
using System.Text;
using System.Threading;

class Program
{
    static void Main(string[] args)
    {
        var arr = arrInt();
        int n = arr[0];
        int m = arr[1];
        var map = new int[m+1];
        arr = arrInt();
        foreach(int ele in arr)
        {
            if(ele % 2 == 1)
            {
                Console.WriteLine(0);
                return;
            }
            int han = ele / 2;
            for (int i = han; i <= m; i += ele) map[i]++;
        }
        var ans = map.Count(v => v == n);
        Console.WriteLine(ans);

    }

    static int[] arrInt()
    {
        return Console.ReadLine().Split(' ').Select(v => int.Parse(v)).ToArray();
    }

}