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;

namespace ABC109C
{
    static class MainClass
    {
        public static void Main(string[] args)
        {

            string[] input1 = Console.ReadLine().Split(' ');
            int N = int.Parse(input1[0]);
            int X = int.Parse(input1[1]);

            string[] input2 = Console.ReadLine().Split(' ');
            var x = new List<int>();
            for (int i = 0; i < N; i++)
            {
                x.Add(int.Parse(input2[i]));
            }

            x.Sort();

            for (int i = 0; i < N - 1; i++)
            {
                x[i + 1] = Gcd(Math.Abs(x[i] - X), Math.Abs(x[i + 1] - X))+X;
            }

            Console.WriteLine(Math.Abs(x[N - 1]-X));

        }


        public static int Gcd(int a, int b){
            int tmp;
            // a<bにする
            if(a >=b){
                tmp = a;
                a = b;
                b = tmp;
            }

            if (a == 0){
                return b;
            }

            tmp = a;
            a = b % a;
            b = tmp;
            return Gcd(a, b);

        }


    }

}