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;

namespace MyProgram{
    class AtCoder{
        static void Main(string[] args){
            long[] input = Array.ConvertAll(Console.ReadLine().Split(' '),long.Parse);
            long N = input[0];
            long X = input[1];
            long[] x = Array.ConvertAll(Console.ReadLine().Split(' '),long.Parse);
            for(var i=0;i<N;i++){
                x[i] += -X;
            }
            for(var i = Gcd(Math.Abs(x[0]),Math.Abs(x[1]==0?x[0]:x[1]));i>0;i--){
                for(var j=0;j<N;j++){
                    if(x[j]%i!=0){
                        break;
                    }
                    if(j==N-1){
                        Console.WriteLine(i);
                        return;
                    }
                }
            }
        }
        static long Gcd(long m,long n){
            long temp;
            while(m%n!=0){
                temp =n;
                n = m%n;
                m = temp;
            }
            return n;
        }
    } 
}