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: Wrong Answer)

using System;
class Program
{
    static void Main(string[] args)
    {
        var t = Read(2);
        var n = t[0]; var f = t[1];
        var x = Read(n);
        for(int i = 0; i < n; i++)
        {
            x[i] -= f;
        }
        Write(gcd(x));
    }

    static void Write(string s) { Console.WriteLine(s); return; }
    static void Write(long n) { Console.WriteLine(n.ToString()); return; }
    static string ReadStr() { return Console.ReadLine(); }
    static string[] ReadStrs() { return Console.ReadLine().Split(' '); }
    static long Read() { return long.Parse(Console.ReadLine()); }
    static long[] Read(long n)
    {
        long[] p = new long[n];
        string[] t = Console.ReadLine().Split(' ');
        for(long i = 0; i < n; i++) { p[i] = long.Parse(t[i]); }
        return p;
    }
    static long abs(long n) { return (n > 0) ? n : -n; }
    static long gcd(params long[] n) { long p = n[0]; for (long i = 1; i < n.Length; i++) { p = gcd(p, n[i]); } return p; }
    static long gcd(long a, long b) { return (a==0)?b:gcd(b % a, a); }
    static long lcm(params long[] n) { long p = n[0]; for (long i = 1; i < n.Length; i++) { p = lcm(p, n[i]); } return p; }
    static long lcm(long a, long b) { return a * b / gcd(a, b); }
    static long max(params long[] n) { long p = n[0]; for (long i = 1; i < n.Length; i++) { p = (p>n[i])?p:n[i]; } return p; }
    static long min(params long[] n) { long p = n[0]; for (long i = 1; i < n.Length; i++) { p = (p<n[i])?p:n[i]; } return p; }
    static void YN(bool t) { Console.WriteLine(t ? "YES" : "NO"); }
    static void Yn(bool t) { Console.WriteLine(t ? "Yes" : "No"); }
    static void yn(bool t) { Console.WriteLine(t ? "yes" : "no"); }
    static string clip(string s, int start, int count)
    {
        if (start + count < s.Length) { s = s.Remove(start + count); }
        if (start > 0) { s = s.Remove(0, start); }
        return s;
    }
    static long ConvToLong(string n, int b)
    {
        long m = 0; long t = 1;
        for (int i = n.Length - 1; i >= 0; i--)
        {
            int k = int.Parse(n[i].ToString());
            m += t * k;
            t *= b;
        }
        return m;
    }
}