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;
import java.util.stream.Stream;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int[] line1 = Stream.of(sc.nextLine().split(" ", 0)).mapToInt(Integer::parseInt).toArray();
		long[] points = Stream.of(sc.nextLine().split(" ", 0)).mapToLong(Long::parseLong).toArray();
		sc.close();
		long ans = Math.abs(points[0] - line1[1]);
		Main main = new Main();
		for (int i = 1; i < line1[0]; i++) {
			ans = main.GCD(ans, Math.abs(points[i] - line1[1]));
		}
		System.out.println(ans);
	}

	public long GCD(long num1, long num2) {
		if (num2 == 0) {
			return num1;
		} else {
			return GCD(num2, num1 % num2);
		}
	}


}