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: Wrong Answer)

import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();
		long g = sc.nextLong()/2;
		int ans = 0;
		boolean flag = true;
		for (int i = 0; i < n-1; i++) {
			long b = sc.nextLong()/2;
			g = lcm(g,b);
			if(g > m) {
				flag = false;
				break;
			}
		}
		if(flag && g%2 == 1) {
			int gcd = (int)g;
			for (int i = 1; i*gcd <= m; i = i+2) {
				ans++;
			}
		}
		System.out.println(ans);
		sc.close();
	}
	public static long gcd(long a, long b) {
		if(a < b) return gcd(b, a);
		if( b == 0) return a;
		return gcd(b, a%b);
	}
	public static long lcm(long a, long b) {
		return a*b/gcd(a, b);
	}
}