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: Accepted)

import java.util.Scanner;
public class Main  {
	static long gcd (long a, long b) {
		long temp;
		while((temp = a%b)!=0) {
			a = b;
			b = temp;
		}
		return b;
	}
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		long M = sc.nextLong();
		long L = 1;
		long A[] = new long[N];
		for(int i = 0 ; i < N ; ++i){
			long a = sc.nextLong();
			A[i] = a;
			long b = a / 2;
			L = (L * b) / gcd(L , b);
			if(M < L){
				System.out.println(0);
				return ;
			}
		}
		for(int i = 0 ; i < A.length ; ++i){
			if(L % A[i] == 0){
				System.out.println(0);
				return ;				
			}
		}
		long ret = 0;
		if(M < L){
			ret = 0;
		}else{
			ret = (M - L) / (2 * L) + 1;
		}
		System.out.println(ret);
	}
}