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.Arrays;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		final int N = sc.nextInt();
		final int X = sc.nextInt();
		int[] x = new int[N+1];
		x[0] = X;
		for (int i = 1; i <=N; i++) {
			x[i] = sc.nextInt();
		}
		// 最大公約数を求める
		Arrays.sort(x);
		int[] y = new int[N];
		for (int i = 0; i < N; i++) {
			y[i] = x[i+1] - x[i];
		}
		int d = y[0];
		if (y.length != 1) {
			for (int i = 1; i < y.length; i++) {
				d = gcd(d, y[i]);
			}
		}
		System.out.println(d);
	}
	private static int gcd(int m, int n) {
	    if(m < n) return gcd(n, m);
	    if(n == 0) return m;
	    return gcd(n, m % n);
	}
}