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.Linq;
using System.Collections.Generic;
class Program
{
	static void Main(string[] args)
	{
	    List<long> input = IO.GetLongList();
	    long n = input[0];
	    long m = input[1];
	    List<long> a = IO.GetLongList();
	    //a.ForEach(k => Console.WriteLine(k));
	    long l = 1;
	    a.ForEach(k=>{
	        l=Lcm(l,k/2);
	    });
	    if(l>m){
           Console.WriteLine(0);
           return;
        }
	    if(a.Any(x => (l/(x/2))%2==0)){
	        Console.WriteLine(0);
	        return;
	    }
	    Console.WriteLine(Math.Ceiling((double)((int)(m/l))/2));
	}
	
	static long Gcd(long a, long b)
    {
        var v = new[] { a, b };
        while (v[1] != 0) { v = new[] { v[1], v[0] % v[1] }; }
        return v[0];
    }
    
    static long Lcm(long a, long b)
    {
        return a / Gcd(a, b) * b;
    }
    
    }

static class IO
{
    static public string GetString() { return Console.ReadLine(); }
    static public int GetInt() { return int.Parse(Console.ReadLine()); }
    static public long GetLong() { return long.Parse(Console.ReadLine()); }
    static public List<string> GetStringList() { return Console.ReadLine().Split(' ').ToList(); }
    static public List<int> GetIntList() { return Console.ReadLine().Split(' ').Select(int.Parse).ToList(); }
    static public List<long> GetLongList() { return Console.ReadLine().Split(' ').Select(long.Parse).ToList(); }
    static public List<double> GetDoubleList() { return Console.ReadLine().Split(' ').Select(double.Parse).ToList(); }
    static public void WriteStrings<T>(IEnumerable<T> values) { foreach (var o in values) { Console.Write(o + " "); } }
}