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 scanner = new Scanner(System.in);

	    int N = Integer.parseInt(scanner.next());
	    long X = Long.parseLong(scanner.next());
	    long[] Y = new long[N];

	    for (int i=0; i<N; i++) {
	    	Y[i] = Math.abs(X - Long.parseLong(scanner.next()));
	    }

	    long a=Y[0];
	    for (int i=1; i<N; i++) {
	    	a=f(a,Y[i]);
	    }
        System.out.print(a);
	}

	public static long f(long m, long n) {
		if (m<n) {
			m= m^n;
			n=m^n;
			m=m^n;
		}

		while (true) {
		     long t = m%n;
		     if(t == 0) {
		    	 break;
		     }
		     m=n;
		     n=t;

		}

		return n;
	}

}