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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Scanner;
import java.math.BigInteger;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Kenji
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        ABC109C solver = new ABC109C();
        solver.solve(1, in, out);
        out.close();
    }

    static class ABC109C {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int N = in.nextInt();
            int X = in.nextInt();
            long[] arr = new long[N + 1];
            for (int i = 0; i < N; i++) {
                arr[i] = in.nextLong();
            }
            arr[N] = X;
            Arrays.sort(arr);
            long ans = 0;
            for (int i = 0; i < N; i++) {
                long a = arr[i];
                long b = arr[i + 1];
                if (i == 0) {
                    ans = b - a;
                } else {
                    ans = gcd(ans, b - a);
                }
            }
            out.println(ans);
        }

        public static long gcd(long m, long n) {
            return BigInteger.valueOf(m).gcd(BigInteger.valueOf(n)).longValue();
        }

    }
}