Problem: There are N cities on a number line. The i-th city is located at coordinate x_i.

Your objective is to visit all these cities at least once.

In order to do so, you will first set a positive integer D.

Then, you will depart from coordinate X and perform Move 1 and Move 2 below, as many times as you like:

* Move 1: travel from coordinate y to coordinate y + D.
* Move 2: travel from coordinate y to coordinate y - D.



Find the maximum value of D that enables you to visit all the cities.

Here, to visit a city is to travel to the coordinate where that city is located.

Constraints

* All values in input are integers.
* 1 \leq N \leq 10^5
* 1 \leq X \leq 10^9
* 1 \leq x_i \leq 10^9
* x_i are all different.
* x_1, x_2, ..., x_N \neq X

Input

Input is given from Standard Input in the following format:


N X
x_1 x_2 ... x_N


Output

Print the maximum value of D that enables you to visit all the cities.

Examples

Input

3 3
1 7 11


Output

2


Input

3 81
33 105 57


Output

24


Input

1 1
1000000000


Output

999999999

Solution (in JAVA):

Solution:
import java.io.InputStream;
import java.io.PrintStream;
import java.util.Arrays;
import java.util.Scanner;

public class Main {
	InputStream in = System.in;
	PrintStream out = System.out;

	int gcd(int a, int b) {
		while (a % b != 0) {
			int tmp = b;
			b = a % b;
			a = tmp;
		}
		return b;
	}

	public void _main(String[] args) {
		Scanner sc = new Scanner(in);

		int N = sc.nextInt();
		int X = sc.nextInt();

		int[] x = new int[N];
		for (int i = 0; i < N; i++) {
			int a = sc.nextInt();
			x[i] = Math.abs(a - X);
		}
		sc.close();

		if (N == 1) {
			out.println(x[0]);
			return;
		}

		Arrays.sort(x);

		int ans = x[0];
		for (int i = 1; i < N; i++) {
			ans = gcd(ans, x[i]);
		}

		out.println(ans);

	}

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

}