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.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int X = sc.nextInt();
        int[] x = new int[n];
        for (int i = 0; i < n ; i++) {
            x[i] = Math.abs(sc.nextInt() - X);
        }
//  全部の最大公約数がＤになるー
        if ( n > 1) {
            int g = gcd(x[0], x[1]);
            for (int i = 1; i < n - 1 ; i++) {
                 g = gcd(g, x[i + 1]);
            }
            System.out.println(g);
        } else {
            System.out.println(x[0]);
        }


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

}