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.*;
import java.math.*;
public class Main{
	public static void main(String[] args){
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		long m=sc.nextLong();
		long l=1;
		int count2=0;
		for(int i=0; i<n; i++){
			long a =sc.nextLong();
			int tmp=0;
			try{
			while(a%2==0){
				a/=2;
				tmp++;
			}
			}catch(StackOverflowError e){
				System.out.println(00);
				return;
			}
			if(i==0){
				count2=tmp;
			}else if(count2!=tmp){
				System.out.println(0);
				return;
			}
			l=l*a/gcd(l,a);
		}
		long two=2;
		count2--;
		try{
		while(count2>0){
			if((count2 & 1)==1){
				l*=two;
			}
			two*=two;
			count2>>=1;
		}
		}catch(StackOverflowError e){
			System.out.println(00);
			return;
		}
		m/=l;
		System.out.println((m+1)/2);
	}
	private static long gcd(long m, long n) {
    if(m < n) return gcd(n, m);
    if(n == 0) return m;
    return gcd(n, m % n);
}
}