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 Java (OpenJDK 11.0.6) (judge verdict: Runtime Error)

import java.util.*;
import java.io.*;

public class Main {
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        long n = sc.nextLong();
        long m = sc.nextLong();
        List<Long> list = new ArrayList<Long>();
        
        for(long i=0;i<n;i++){
            long a = sc.nextLong();
            list.add(a);
        }
        while(list.size() != 1){
            list.add(lcm(list.get(0),list.get(1)));
            list.remove(0);
            list.remove(0);
        }
        if(list.get(0)>=m){
            System.out.println("0");
            System.exit(0);
        }
        int kisu=0;
        
        long n1 = (long)((double)m/(double)list.get(0));
        long n2 = (long)((double)m/(double)list.get(0)+(double)0.5);
 
        if(n2-n1 == 1)kisu=1;
        System.out.println(m/list.get(0)+kisu);
    }
    
    static long gcd(long a,long b){
        if(b==0)return a;
        return gcd(b,a%b);
    }
    
    static long lcm(long a,long b){
        long a2,b2;
        if(a<b){a2=b;b2=a;}
        else {a2=a;b2=b;}
        long c = gcd(a2,b2);
        return a*b/c;
    }
    
}