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: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;
using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute;
using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions;
public static class P
{
    public static void Main()
    {
        var nm = Console.ReadLine().Split().Select(int.Parse).ToArray();

        var n = nm[0];
        var m = nm[1];
        var a = Console.ReadLine().Split().Select(long.Parse).ToArray();
        var gcd = a.Aggregate(GCD);
        var lcm = a.Aggregate(LCM);
        if (lcm / gcd % 2 == 0)
        {
            Console.WriteLine(0);
            return;
        }
        lcm /= 2;
        Console.WriteLine((m / lcm + 1) / 2);
    }

    static long GCD(long a, long b)
    {
        while (true)
        {
            if (b == 0) return a;
            a %= b;
            if (a == 0) return b;
            b %= a;
        }
    }

    static long LCM(long a, long b) 
    {
        var res = a / GCD(a, b) * b;
        if (int.MaxValue < res) return 0;
        return res;
    }
}