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.ArrayList;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N=sc.nextInt();
		int M=sc.nextInt();
		ArrayList<Integer> listA = new ArrayList<>();
		for(int i=0;i<N;i++) {
			listA.add(sc.nextInt());
		}
		
		boolean flag = true;
		for(int i=0;i<N-1;i++) {
			if(divCountByTwo(listA.get(i))!=divCountByTwo(listA.get(i+1))) {
				flag = false;
				break;
			}
		}
		
		
		if(flag) {
			int T = lcm(listA)/2;
			int tmp = M/T;
			if(tmp%2==1) {
				System.out.println(tmp/2+1);
			}else {
				System.out.println(tmp/2);
			}
		}else {
			System.out.println(0);
		}
		
		
	}
	
	static boolean isOddAndPlus(int n) {
		if(n%2==1 && (n-1)/2>=0) {
			return true;
		}else{
			return false;
		}
	}

	static int divCountByTwo(int n) {
		if(n%2>0) {
			return 0;
		}else {
			return 1+divCountByTwo(n/2);
		}
	}
	
	static int gcd(int a,int b) {
		if(a<b) {
			return gcd(b,a);
		}else if(b==0){
			return a;
		}else {
			return gcd(b,a%b);
		}
	}
	
	static int lcm(int a,int b) {
		return a*b/gcd(a,b);
	}
	
	static int lcm(ArrayList<Integer> list) {
		if(list.size()==2) {
			return lcm(list.get(0),list.get(1));
		}else {
			int tmp1 = list.remove(list.size()-1);
			int tmp2 = list.remove(list.size()-1);
			list.add(lcm(tmp1,tmp2));
			return lcm(list);
		}
	}

}