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) {
		try (Scanner scanner = new Scanner(System.in)) {
			int n = scanner.nextInt(), k = scanner.nextInt();
			int gcd = 0;
			for (int i = 0; i < n; i++) {
				int x = scanner.nextInt();
				if (x != k) {
					if (0 == gcd) {
						gcd = Math.abs(x - k);
					} else {
						gcd = gcd(gcd, Math.abs(x - k));
					}
				}
			}
			System.out.println(gcd);
		}
	}

	/**
	 * mとnの最大公約数を返す
	 * 
	 * @param m
	 * @param n
	 * @return mとnの最大公約数
	 */
	private static int gcd(int m, int n) {
		if (0 == n) {
			return m;
		}
		return gcd(n, m % n);
	}
}