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 static System.Math;
using System.Linq;
 
class DandA {
    static void Main(string[] args) {
        int[] nm = ReadLineIntArray();
        int[] aList = ReadLineIntArray();
        int[] resultArray = aList.Distinct().ToArray();
        Array.Sort(resultArray);
      　int intMax = resultArray.Max();
        int half = intMax / 2;
        int product = 0;
        int cnt = 0;
        int i = 1;
        while (nm[1] >= half + product) {
            bool flg = true;
            for (int wk = resultArray.Length - 1; wk >= resultArray.Length / 2;wk--) {
                if (((half + product) - (resultArray[wk] / 2)) % resultArray[wk] != 0) {
                    flg = false;
                    break;
                }
            }
            if (flg) {cnt++;}
            product = intMax * i;
            i++;
        }
        Console.WriteLine(cnt);
    }
  
    static private string ReadLineStr() {return Console.ReadLine();}
    static private int ReadLineInt() {return int.Parse(Console.ReadLine());}
    static private string[] ReadLineStrArray() {return Console.ReadLine().Trim().Split();}
    static private int[] ReadLineIntArray() {return Console.ReadLine().Trim().Split().Select(a => int.Parse(a)).ToArray();}
    static private string[][] ReadMLineStrArray(int arg) { return new int[arg].Select(_ => Console.ReadLine().Split()).ToArray();}
    static private int[][] ReadMLineIntArray(int arg) { return new int[arg].Select(_ => Console.ReadLine().Split().Select(int.Parse).ToArray()).ToArray();}
}