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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace C_Skip
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] NX = Console.ReadLine().Split(' ');
            int N = int.Parse(NX[0]);
            int X = int.Parse(NX[1]);

            List<int> num = new List<int>
            {
                X
            };
            int x;
            string[] x0 = Console.ReadLine().Split(' ');

            for (int i = 0; i < N; i++)
            {
                x = int.Parse(x0[i]);
                num.Add(x);
            }
            
            num.Sort();
            List<int> sa = new List<int>();

            for (int i = 0; i < N; i++)
            {
                sa.Add(num[i + 1] - num[i]);
            }

            int gcd = 0;
            List<int> gcdList = new List<int>();

            for (int i = 0; i < N-1; i++)
            {
                gcd = Gcd(sa[i + 1], sa[i]);
                gcdList.Add(gcd);
            }
            Console.WriteLine(gcdList.Min());
        }

        // ユークリッドの互除法 
        public static int Gcd(int a, int b)
        {
            if (a < b)
                // 引数を入替えて自分を呼び出す
                return Gcd(b, a);
            while (b != 0)
            {
                var remainder = a % b;
                a = b;
                b = remainder;
            }
            return a;
        }
    }
}