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;

namespace solve
{
    class Program
    {
        static void Main(string[] args)
        {
            var NM = Console.ReadLine().Split(new char[] { ' ' }).Select(x => long.Parse(x)).ToArray();
            var Bs = Console.ReadLine().Split(new char[] { ' ' }).Select(x => long.Parse(x) / 2).ToArray();
            var X = LcmFromArray(Bs);

            var found = false;
            for (var i = 0; i < NM[0]; i++)
            {
                if ((X / Bs[i]) % 2 == 0)
                {
                    Console.WriteLine(0);
                    found = !found;
                    break;
                }
            }
            if (!found)
            {
                Console.WriteLine((NM[1] / X + 1) / 2);
            }
        }

        public static long ComputeGcd(long a, long b)
        {
            if (a < b)
            {
                var temp = a;
                a = b;
                b = temp;
            }
            while (a % b != 0)
            {
                var temp = a;
                a = b;
                b = temp % b;
            }

            return b;
        }

        public static long ComputeLcm(long a, long b)
        {
            return a * b / ComputeGcd(a, b);
        }

        public static long LcmFromArray(long[] As)
        {
            var ans = As[0];
            for (var i = 1; i < As.Length; i++)
            {
                ans = ans * As[i] / ComputeGcd(ans, As[i]);
            }
            return ans;
        }
    }
}