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: Accepted)


import java.util.Scanner;

public class Main {

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

	private long f(int x) {
		long res = 0;
		while(x % 2 == 0) {
			x /= 2;
			res++;
		}
		return res;
	}

	private long gcd(long x, long y) {
		if(y == 0) return x;
		return gcd(y, x % y);
	}

	private long lcm(long x, long y) {
		return x / gcd(x,y) *  y;
	}

	public void run() {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();
		int a[]=new int[n];
		for(int i=0; i<n; i++) {
			a[i]=sc.nextInt();
		}
		for(int i=0; i<n; i++) {
			a[i] /= 2;
		}
		long t = f(a[0]);
		for(int i=0; i<n; i++) {
			if(t != f(a[i])) {
				System.out.println(0);
				sc.close();
				return;
			}
		}
		long l=1;
		for(int i=0; i<n; i++) {
			l = lcm(l, a[i]);
		}
		if(l>m) {
			System.out.println(0);
			sc.close();
			return;
		}
		long ans = m/l;
		ans = (ans+1)/2;
		System.out.println(ans);

		sc.close();
	}
}