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 {

    Scanner sc = new Scanner(System.in);

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

    void run() {

        int n = sc.nextInt();
        int m = sc.nextInt();
        int[] arr = new int[n];
        for (int i=0; i<n; i++) arr[i] = sc.nextInt();
        int[] diff = new int[n];
        for (int i=0; i<n; i++) {
            diff[i] = Math.abs(arr[i] - m);
        }

        int res = diff[0];

        for (int i=1; i<n; i++) {
            res = gcd(res, diff[i]);
        }

        System.out.println(res);

    }

    int gcd(int m, int n) {
        if (n == 0) return m;
        return gcd(n, m%n);
    }


}