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.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int m = sc.nextInt();
        int base = sc.nextInt() / 2;
        HashSet<Integer> set = new HashSet<>();
        for (int i = 1; i < n; i++) {
            set.add(sc.nextInt() / 2);
        }
        set.remove(base);
        int count = getDev2Count(base);
        int org = base;
        for (int x : set) {
            if (count != getDev2Count(x)) {
                System.out.println(0);
                return;
            }
            org = gcd(org, x);
        }
        long lcm = base / org;
        for (int x : set) {
            lcm *= x / org;
            if (lcm > m) {
                System.out.println(0);
                return;
            }
        }
        System.out.println((m / lcm + 1) / 2);
    }
    
    static int getDev2Count(int x) {
        int count = 0;
        while (x % 2 == 0) {
            count++;
            x /= 2;
        }
        return count;
    }
    
    static int gcd(int x, int y) {
        if (x % y == 0) {
            return y;
        } else {
            return gcd(y, x % y);
        }
    }
}