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.Text;
using System.Collections.Generic;
using static System.Math;
using System.Linq;
using static System.Array;
using System.Runtime.Serialization.Formatters.Binary;
using System.IO;

namespace AtcoderExpress
{


    class Program2
    {
        static long[] A;
        static void Main(string[] args)
        {
            var NM = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
            var N = NM[0];
            var M = NM[1];
            var flg = true;
            A= Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();

            var Div2Count = 0;
            var CopyA1 = A[0];
            while (CopyA1 % 2 == 0)
            {
                CopyA1 /= 2;
                Div2Count++;
            }

            for (int i = 0; i < N; i++)
            {
                var Count  = 0;
                var CopyAi = A[i];
                while(CopyAi%2 == 0)
                {
                    CopyAi /= 2;
                    Count++;
                }

                if(Count != Div2Count)
                {
                    flg = false;
                    break;
                }
            }

            for (int i = 0; i < A.Length; i++)
            {
                A[i] /= 2;
            }

            var LCM = A[0];
            for (int i = 1; i < N; i++)
            {
                LCM = lcm(LCM,A[i]);
            }
            //Console.WriteLine( LCM);
            if (flg)
            {
                Console.WriteLine((M/LCM+1)/2);
            }
            else
            {
                Console.WriteLine(0);
            }
        }

        static long lcm(long a,long b)
        {
            return (a * b / gcd(a, b));
        }
        

        static long gcd(long a, long b)
        {
            if (a < b) return gcd(b, a);
            if( b > 0)
            {
                return gcd(b, a%b);
            }
            else
            {
                return a;
            }
        }
    }
}