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.Linq;
using System.Collections.Generic;

class Program
{
    static void Main(string[] args)
    {
        var inputs = Console.ReadLine().Split(' ');
        var N = int.Parse(inputs[0]);
        var X = long.Parse(inputs[1]);
        inputs = Console.ReadLine().Split(' ');
        var x = new long[N];
        for (int i = 0; i < N; i++)
        {
            x[i] = long.Parse(inputs[i]);
        }

        x = x.OrderBy(xd => xd).ToArray();
        var d = new long[N];
        // スタート地点から、最初、あるいは末尾までの移動する最大公約数
        var gcd = Math.Max(Math.Abs(x.First() - X), Math.Abs(x.Last() - X));
        for (int i = 1; i < N; i++)
        {
            d[i] = Math.Abs(x[i] - x[i - 1]);
            gcd = Gcd(d[i], gcd);
        }
        Console.WriteLine(gcd);
    }

    /**
     * 最小公倍数
     * <see cref="https://qiita.com/gushwell/items/f08d0e71fa0480dbb396"/>
     */
    public static long Lcm(long a, long b)
    {
        return a * b / Gcd(a, b);
    }

    /**
     * ユークリッド互除法(最大公約数)
     * <see cref="https://qiita.com/gushwell/items/e9614b4ac2bea3fc6486"/>
     */
    public static long Gcd(long a, long 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;
    }
}