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.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int N = in.nextInt();
		if (N <= 1) {
			System.out.println(0);
			return;
		}
		long M = in.nextLong();
		long[] a = new long[N];
		for (int i = 0; i < N; i++) {
			a[i] = in.nextLong() / 2l;
		}
		long x = a[0];
		for (int i = 1; i < N; i++) {
			x = lcm(x, a[i]);
			if (x > M) {
				System.out.println(0);
				return;
			}
		}

		long count = 0;
		for (long i = 1; (i * x) <= M; i += 2l) {
			count++;
		}
		System.out.println(count);
		in.close();
	}

	static long gcd(long x, long y) {
		if (x < y) {
			long tmp = y;
			y = x;
			x = tmp;
		}
		if (y == 0) {
			return x;
		}
		return gcd(x % y, y);
	}

	static long lcm(long m, long n) {
		return m * n / gcd(m, n);
	}
}