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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Convert;
using static System.Math;
//using static System.Globalization.CultureInfo;

class Program
{
    static void Main(string[] args)
    {
        var nx = Add.ar;
        var xs = Add.ar;
        xs = xs.Select(v => Abs(v - nx[1])).ToArray();
        var gcd = xs[0];
        for (var i = 1; i < nx[0]; i++)
            gcd = Calculation.GCD(gcd, xs[i]);
        WriteLine(gcd);
    }
}

public class Add
{
    public static string read => ReadLine();
    public  static int[] ar => Array.ConvertAll(read.Split(' '), int.Parse);
    public  static int num => ToInt32(read);
    public  static long[] arL => Array.ConvertAll(read.Split(' '), long.Parse);
    public  static long numL => ToInt64(read);
    public  const string Alfa = "abcdefghijklmnopqrstuvwxyz";
    public  const int MOD = 1000000007;
}

public class Calculation
{
    public static int LCM(int num1, int num2)
    {
        return num1 / GCD(num1, num2) * num2;
    }

    public static long LCM(long num1, long num2)
    {
        return num1 / GCD(num1, num2) * num2;
    }

    public static int GCD(int num1, int num2)
    {
        return num1 < num2 ? GCD(num2, num1) :
            num2 > 0 ? GCD(num2, num1 % num2) : num1;
    }

    public static long GCD(long num1, long num2)
    {
        return num1 < num2 ? GCD(num2, num1) :
            num2 > 0 ? GCD(num2, num1 % num2) : num1;
    }
}