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.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ABC150
{
    class D
    {
        static void Main(string[] args)
        {
            int ans = 0;
            int f = 1;
            int[] nm = Console.ReadLine().Split().Select(int.Parse).ToArray();
            int[] a= Console.ReadLine().Split().Select(int.Parse).ToArray();
            int[] b = new int[nm[0]];
            for (int i = 0; i < nm[0]; i++)
            {
                b[i] = a[i] / 2;
                if (b[i] % 2 == 0) { f = 0; }
            }
            int hl = (int)Lcm(b);
            ans = ((nm[1] / hl) + 1) / 2;
            Console.WriteLine(ans*f);
        }
        public static long Lcm(long m,long n)
        {
            return m * n / Gcd(m, n);
        }
        public static long Gcd(long m, long n)
        {
            long temp;
            while (m % n != 0)
            {
                temp = n;
                n = m % n;
                m = temp;
            }
            return n;
        }
        public static long Lcm(int[] n)
        {
            if (n.Length == 2) { return Lcm(n[0], n[1]); }
            return Lcm(Lcm(n.Take(n.Length - 1).ToArray()), n[n.Length - 1]);
        }
    }
}