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;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {            
            string[] strNM = Console.ReadLine().Split(' ');
            string[] strA = Console.ReadLine().Split(' ');

            long N = long.Parse(strNM[0]);
            long M = long.Parse(strNM[1]);

            long[] a = new long[N];
            for(long i = 0; i < N; i++)
            {
                a[i] = long.Parse(strA[i]) / 2;
            }
            long koubai = a[0];

            for(long i = 1; i < N; i++)
            {
                koubai = saidaikoubai(koubai, a[i]);
            }

            long ans = (M / koubai) / 2 + (M / koubai) % 2;

            Console.WriteLine(ans);
        }
       
        static long saidaikouyaku(long a, long b)
        {
            long ans = 0;
            if(a < b)
            {
                long tmp = a;
                a = b;
                b = tmp;
            }

            long r = a % b;
            while(r != 0)
            {
                a = b;
                b = r;
                r = a % b;
            }

            return b;
        }
        static long saidaikoubai(long a, long b)
        {
            long ans = a * b / saidaikouyaku(a, b);
            return ans;
        }
    }
}




/*
  long N = long.Parse(Console.ReadLine());
            string[] strP = Console.ReadLine().Split(' ');
            string[] strQ = Console.ReadLine().Split(' ');

            long[] P = new long[N];
            long[] Q = new long[N];
            for(long i = 0; i < N; i++)
            {
                P[i] = long.Parse(strP[i]);
                Q[i] = long.Parse(strQ[i]);
            }




            Console.WriteLine(ans);
 * */