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.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;

namespace D
{
    public class Program
    {
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();
            Console.Out.Flush();
        }

        public static void Solve()
        {
            var nm = Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray();
            var ai = Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray();
            var p = ai.Distinct()
            .Select(x => x % 2 == 0 ? x / 2 : 0)
            .Aggregate(1, (x, y) => (x * y != 0) ? LCM(x, y) : 0);
            if (p == 0)
            {
                Console.WriteLine(0);
                return;
            }
            Console.WriteLine((nm[1] / (p * 2)) + (nm[1] % (p * 2)) / p);
        }

        static int GCD(int a, int b) => b == 0 ? a : GCD(b, a % b);
        static int LCM(int a, int b) => a * b / GCD(a, b);
    }
}