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: Wrong Answer)

import java.util.Arrays;
import java.util.Scanner;
import java.util.stream.IntStream;

public class Main {

	public static void main(String[] args) {
		try (Scanner scanner = new Scanner(System.in)) {
			int n = scanner.nextInt();
			long m = scanner.nextLong();
			int[] a = new int[n];
			IntStream.range(0, n).forEach(i -> a[i] = scanner.nextInt() / 2);
			int min = Arrays.stream(a).min().getAsInt();
			long lcm = 1, gcd = a[0];
			for (int ai : a) {
				gcd = gcd(gcd, ai);
				lcm = lcm(lcm, ai);
				if (lcm > m) {
					System.out.println(0);
					return;
				}
			}
			if ((min > 1) && (gcd == min)) {
				System.out.println(0);
				return;
			}
			long count = m / lcm;
			System.out.println((count + 1) / 2);
		}
	}

	// 最小公倍数lcm
	private static long lcm(long a, long b) {
		return a / gcd(a, b) * b;
	}

	// 最大公約数
	private static long gcd(long a, long b) {
		if (a < b)
			return gcd(b, a);
		if (b == 0)
			return a;
		return gcd(b, a % b);
	}
}