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.*;

public class Main {
	Scanner sc = new Scanner(System.in);
	final int MOD = 1000000007;
	final int MAX = Integer.MAX_VALUE;
	final long LMAX = Long.MAX_VALUE;
	int LEN = (int)1e6 + 1;
	void doIt() {
		int N = sc.nextInt();
		int M = sc.nextInt();
		int a[] = new int[N];

		for(int i = 0; i < N; i++)
			a[i] = sc.nextInt();
		int count = numTwo(a[0]);
		for(int i = 1; i < N; i++) {
			if(count != numTwo(a[i])) {
				System.out.println(0);
				return;
			}
		}

		long lcm = a[0];
		for(int i = 1; i < N; i++) {
			long g = gcd(lcm, a[i]);
			lcm = lcm * a[i] / g / 2;
			if(lcm / 2 > M) {
				System.out.println(0);
				return;
			}
		}
		long ans = M / (lcm / 2) - M / lcm;
		System.out.println(ans);

	}


	int numTwo(int n) {
		int cnt = 0;
		while(n % 2 == 0) {
			cnt++;
			n /= 2;
		}
		return cnt;
	}
	
	long gcd(long a, long b) {
		return (b == 0)?a:gcd(b, a % b);
	}

	public static void main(String[] args) {
		new Main().doIt();
	}

}