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 {
    static Scanner sc = new Scanner(System.in);

    public static void main(String[] args) {
        int n = sc.nextInt();
        int m = sc.nextInt();
        Set<Long> set = new HashSet<>();
        for (int i = 0; i < n; i++) {
            set.add(sc.nextLong() / 2);
        }
        long lcd = 1;
        Iterator<Long> iter = set.iterator();
        if (set.size() > 1) {
            long k = gcd(iter.next(), iter.next());
            while(iter.hasNext())
            {
                k = gcd(k, iter.next());
            }
            for(long i : set)
            {
                lcd *= i;
                lcd /= k;
            }
        } else {
            lcd = iter.next();
        }
        System.out.println((m / lcd + 1) / 2);
    }



    private static long gcd(long a, long b) {
        if(a == 0||b == 0)
            return 0;
        long k = a % b;
        while(k != 0)
        {
            k = a % b;
            a = b;
            b = k;
        }
        return a;
    }
}