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 data[] = new int[n];
      int data2[] = new int[n];

      for (int i  = 0;i<n ;i++ ) {
        data[i] = sc.nextInt();
      }

      for (int i  = 0;i<n ;i++ ) {
        data2[i] = Math.abs(data[i]-x);
      }

      System.out.println(gcd(data2,n));

  }

    static int gcd(int[] data2,int n){
      Arrays.sort(data2);
      int ans = data2[0];
      for (int i = 0;i<n ;i++ ) {
        if (ans<data2[i]) {
          int temp = ans;
          ans = data2[i];
          data2[i] = temp;
        }
        while(data2[i]>0){
          int r = ans%data2[i];
          ans = data2[i];
          data2[i] = r;
        }
       }
       return ans;
      }

    }