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.Text;
using System.Numerics;
using System.IO;

namespace SolutionCS
{
    class Program
    {
        static int gcd(int a, int b)
        {
            if (a < b)
            {
                return gcd(b, a);
            }

            while (b != 0)
            {
                int rem = a % b;
                a = b;
                b = rem;
            }

            return a;
        }

        static void Main(string[] args)
        {
            string[] strs = Console.ReadLine().Split(' ');
            int N = int.Parse(strs[0]);
            int X = int.Parse(strs[1]);

            strs = Console.ReadLine().Split(' ');
            int[] h = new int[N+1];
            for (int i = 0; i < N; i++)
            {
                h[i] = int.Parse(strs[i]);
            }
            h[N] = X;

            Array.Sort(h);

            int ans = Math.Abs(h[1] - h[0]);
            for (int i = 2; i < N + 1; i++)
            {
                ans = gcd(ans, Math.Abs(h[i] - h[i - 1]));
            }

            Console.WriteLine(ans);
        }
    }
}