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 System.Text;
using System.Threading.Tasks;

namespace test
{
    class Program
    {
        static void Main(string[] args)
        {
            var input = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
            var N = input[0];
            var X = input[1];
            var city = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
            var dis = new int[N];
            for (int i = 0; i < N; i++) dis[i] = Math.Abs(X - city[i]);
            var ans = 0;
            if (N == 1) ans = dis[0];
            else ans = Gcd(dis[0], dis[1]);
            for (int i = 2; i < N; i++) ans = Gcd(ans, dis[i]);

            Console.WriteLine(ans);
        }

        public static int Gcd(int a, int b)
        {
            if (b == 0) return a;

            return Gcd(b, a % b);
        }

        public static int Lcm(int a, int b)
        {
            return a * b / Gcd(a, b);
        }
    }
}