Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

3 3
1 7 11

Sample Output 1

2

Setting D = 2 enables you to visit all the cities as follows, and this is the maximum value of such D.

Perform Move 2 to travel to coordinate 1.

Perform Move 1 to travel to coordinate 3.

Perform Move 1 to travel to coordinate 5.

Perform Move 1 to travel to coordinate 7.

Perform Move 1 to travel to coordinate 9.

Perform Move 1 to travel to coordinate 11.

Sample Input 2

3 81
33 105 57

Sample Output 2

24

Sample Input 3

1 1
1000000000

Sample Output 3

999999999

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;

public class Main {

    public static void main(String[] args) {


        Scanner scan = new Scanner(System.in);
        int N = Integer.parseInt(scan.next());
        long X = Integer.parseInt(scan.next());

        long distance;
        long[] distanceArray = new long[N];
        for(int i = 0; i < N; i++){
            distance = Long.parseLong(scan.next()) - X;
            if(distance < 0) distance = -(distance);
            distanceArray[i] = distance;
        }

        Arrays.sort(distanceArray);

        if(distanceArray.length == 1){

            System.out.println(distanceArray[0]);

        }else{

            System.out.println(gcd(distanceArray[1], distanceArray[0]));
        }

    }

    private static long gcd(long a, long b){

        if(a%b == 0){

            return b;

        }else{

            return gcd(b, a%b);

        }
    }
}