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: Time Limit Exceeded)

using System;
using System.Linq;

namespace D
{
    class Program
    {
        static void Main(string[] args)
        {
            Console.WriteLine(solver());
        }
        static long solver()
        {
            var NM = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
            var N = NM[0]; var M = NM[1];
            var A = Array.ConvertAll(Console.ReadLine().Split(' '), long.Parse);
            var halfA = A.Select(n => n / 2).ToArray();
            var minimumSCM = halfA[0];
            for (int i = 1; i < N; i++) minimumSCM = halfA[i] / GCD(minimumSCM, halfA[i]) * minimumSCM;
            for (int i = 0; i < N; i++) if (((minimumSCM / halfA[i]) % 2) == 0) return 0;
            if (((M / minimumSCM) % 2) == 0) return M / minimumSCM / 2;
            else return M / minimumSCM / 2 + 1;
        }
        static long GCD(long A, long B)
        {
            if (B > A) return GCD(B, A);
            if (A % B == 0)
            {
                return B;
            }
            else
            {
                return GCD(B, A % B);
            }
        }
    }
}