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 Go (1.6) (judge verdict: Wrong Answer)

package main

import (
	"fmt"
	"sort"
)

func main() {
	var n, x int
	fmt.Scan(&n, &x)

	var xx = make([]int, n)
	for i := range xx {
		fmt.Scan(&xx[i])
	}
	xx = append(xx, x)
	sort.Ints(xx)
	if x == 1 {
		fmt.Println(xx[1] - x)
		return
	}

	var deff_temp []int
	var deff []int
	var maxD int
	for i := 0; i < n; i++ {
		temp := xx[i] - xx[i+1]
		if temp < 0 {
			deff_temp = append(deff_temp, -temp)
		} else {
			deff_temp = append(deff_temp, temp)
		}
	}
	sort.Ints(deff_temp)
	for i := 0; i < len(deff_temp); i++ {
		if deff_temp[i] != 0 {
			deff = append(deff, deff_temp[i])
		}
	}
	maxD = deff[0]
	for i := 0; i < len(deff); i++ {
		////////////////
		if deff[i]%deff[0] != 0 {
			if deff[0]%2 == 0 && deff[i]%2 == 0 {
				maxD = 2
			} else if deff[0]%3 == 0 && deff[i]%3 == 0 {
				maxD = 3
			} else if deff[0]%5 == 0 && deff[i]%5 == 0 {
				maxD = 5
			}
		}
	}
	fmt.Println(maxD)

}