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.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int Zahyou = sc.nextInt();

		List<Integer> list = new ArrayList<>();
		for(int i = 0; i < N; i++) {
			list.add(sc.nextInt());
		}
		list.add(Zahyou);
		Collections.sort(list);


		int kyori = 1000000001;
		int num = 0;
		for(int i = 0; i < N; i++) {
			num = Math.abs(list.get(i+1)-list.get(i));

			if(num == 0) {
				continue;
			}
			if(kyori == 1000000001) {
				kyori = num;
				continue;
			}
			kyori = gcd(kyori,num);

		}

		if(kyori == 1000000001) {
			kyori = 0;
		}
		System.out.println(kyori);
		sc.close();
	}


	//最大公約数gcd
	static int gcd (int a, int b) {
		if(b == 0) {
			return a;
		}
		if(b % a == 0) {
			return a;
		}
		if(a % b == 0) {
			return b;
		}

		int temp;
		while((temp = a%b)!=0) {
			a = b;
			b = temp;
		}
		return b;
	}

}