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.util.*;

public class Main {

    public static void main(String args[]) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int x = sc.nextInt();
        int[] a = new int[n + 1];
        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();
        }
        a[n] = x;
        Arrays.sort(a);
        for (int i = 0; i <= n; i++) {
            a[i] -= x;
        }
        for (int i = 1; i <= n; i++) {
            a[i] -= a[0];
        }
        a[0] = 0;
        int ans = a[1] - a[0];
        for (int i = 2; i <= n; i++) {
            ans = gcd(ans, a[i] - a[i - 1]);
        }
        System.out.println(ans);

    }

    public static int gcd(int a, int b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }

}