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[] x = new int[n];
    int[] y = new int[n];
    for(int i = 0; i < n; i++) {
      x[i] = sc.nextInt();
      y[i] = Math.abs(x[i] - X);
    }
    int d = 0;
    if(n == 1) {
      d = y[0];
    } else {
      d = gcd(y[0], y[1]);
      for(int i = 2; i < n; i++) {
        d = gcd(d, y[i]);
      }
    }
    System.out.println(d);
  }

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