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: Accepted)

import java.util.*;
import java.io.*;
import java.math.BigInteger;
 
public class Main {
	public static long twoCount(long a){
		long count = 0;
		while(a%2 == 0){
			a = a/2;
			count++;
		}
		return count;
	}

	private static long calcGcd(long m, long n) {
        if (m <= 0 || n <= 0) {
            throw new IllegalArgumentException("Arguments must be 1 and over.");
        }
        if(m < n) {
            long tmp = m;
            m = n;
            n = tmp;
        }
        long remainder = 0;
        while ((remainder = m % n) != 0) {
            m = n;
            n = remainder;
        }
        return n;
    }

    private static long calcLcm(long m, long n) {
        return m * n / calcGcd(m, n);
    }
	
	public static void main(String[] args) {
	Scanner s = new Scanner(System.in);
	int N = s.nextInt();
	int M = s.nextInt();
	long[] A = new long[N];
	for(int i = 0; i < N; i++){
		A[i] = s.nextInt()/2;
	}

	boolean isExist = true; 
	for(int i = 0; i < N-1; i++){
		if(twoCount(A[i]) != twoCount(A[i+1])) isExist = false;
	}
	

	if(isExist){
		long maxLcm = A[0];
		boolean swi = false;
		for(int i = 0; i < N; i++){
			maxLcm = calcLcm(A[i], maxLcm);
			if(maxLcm > M){
				swi = true;
				break;
			}
		}
		if(swi){
			System.out.println(0);
		}else{
			System.out.println((M/maxLcm+1)/2);
		}
	}else{
		System.out.println(0);
	}
    
  }
}