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: Wrong Answer)

import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		
		Scanner in = new Scanner(System.in);
		
		int N = in.nextInt();
		int S = in.nextInt();
		
		int[] x = new int[N+1];
		int[] y = new int[N+1];
		
		int min = Integer.MAX_VALUE;
		int key = -1;
		
		for (int i=1;i<=N;i++)
		{
			x[i]= in.nextInt();
			y[i]= Math.abs(x[i] - S);
			
				if ( y[i] < min)
				{
					min = y[i];
					key = i;
				}
		}
		
		
		
		int D=min;
		
		while (D>=1) {
			for (int i=1;i<=N;i++) {
				if (y[i]%D!=0) {
					D--;
					break;
				}
			}
			System.out.println(D);
			break;
		}
	}
}