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;

class D
{
	static int[] Read() => Console.ReadLine().Split().Select(int.Parse).ToArray();
	static void Main()
	{
		var h = Read();
		int n = h[0], m = h[1];
		var a = Read().Distinct().Select(x => x / 2).ToArray();

		long lcm = a[0];
		for (int i = 1; i < a.Length; i++)
		{
			lcm = Lcm(lcm, a[i]);
			if (lcm > m) { Console.WriteLine(0); return; }
		}

		if (a.Any(x => lcm / x % 2 == 0)) { Console.WriteLine(0); return; }
		Console.WriteLine((int)((m / lcm + 1) / 2));
	}

	static long Gcd(long x, long y) { for (long r; (r = x % y) > 0; x = y, y = r) ; return y; }
	static long Lcm(long x, long y) => x / Gcd(x, y) * y;
}