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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Linq;

class Program
{
    static void Main(string[] args)
    {
        var input1 = Console.ReadLine().Split().Select(x => long.Parse(x)).ToArray();
        var input2 = Console.ReadLine().Split().Select(x => long.Parse(x)).ToList();
        var _N = input1[0];
        var _M = input1[1];
        var _aList = input2.Distinct().OrderBy(x => -x).Select(x => x / 2).ToArray();
        long total = 1;
        for(var i = 0; i < _aList.Count(); i++)
        {
            total = Lcm(total, _aList[i]);
        }
        long ans = 0;
        var tmp = total % 2 == 0 ? total / 2 : total;
        if(total != 1)
        {
            ans = (_M / total);
            ans = (ans / 2) + (ans % 2);
        }

        Console.WriteLine(ans);
        Console.ReadLine();
    }

    public static long Lcm(long a, long b) => a * b / Gcd(a, b);
    public static long Gcd(long a, long b) => a > b ? GcdRecursive(a, b) : GcdRecursive(b, a);
    static long GcdRecursive(long a, long b) => b == 0 ? a : GcdRecursive(b, a % b);
}