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 Java7 (OpenJDK 1.7.0) (judge verdict: Runtime Error)

import java.util.*;
import java.lang.*;

public class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        long m = sc.nextLong();
        int[] a = new int[n];
        for(int i = 0;i<n;i++){
            a[i] = (sc.nextInt() / 2);
            if((sc.nextInt() / 2) % 2 == 0){System.out.println(0);return;}
        }
        Arrays.sort(a);
        long result = a[0];
        for(int i = 1;i<n;i++){
            result = (result * (long)a[i]) / gcd(result,(long)a[i]);
        }
        long num = 1;
        if(result>m){System.out.println(0);}
        else{
            m -= result;
            num += ((m/result)/2);
            System.out.println(num);
        }
        sc.close();
    }

    static long gcd (long x,long y) {return y>0?gcd(y,x%y):x;}

}