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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.util.*;

public class Main{
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		
		int N, M, lcm;
		N = in.nextInt();
		M = in.nextInt();
		lcm = 1;
		for (int i = 0; i < N; i++)
		{
			int temp = in.nextInt();
			int gcd = 1;
			for (int j = 1; j <= temp && j <= lcm; ++j)
			{
				if(temp % j == 0 && lcm % j == 0)
					gcd = j;
			}
			
			lcm = (temp * lcm) / gcd;
		}
		lcm /= 2;
		System.out.println(M/lcm - M/(lcm*2));
	}
}