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: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"sort"
	"strconv"
)

func main() {
	var n, x int
	s := wordScanner(100)
	scanInts(s, &n, &x)
	l := scanIntSlice(s, n)

	sort.Ints(l)
	d := make([]int, n)
	for i, xi := range l {
		d[i] = abs(x - xi)
	}

	ans := d[0]
	for _, di := range d {
		ans = gcd(ans, di)
	}

	fmt.Println(ans)
}

func gcd(x, y int) int {
	for x%y != 0 {
		x, y = y, x%y
	}
	return y
}

func abs(x int) int {
	if x < 0 {
		return -x
	}
	return x
}

func wordScanner(n int) *bufio.Scanner {
	s := bufio.NewScanner(os.Stdin)
	s.Split(bufio.ScanWords)
	b := make([]byte, n)
	s.Buffer(b, n)
	return s
}

func scanInts(s *bufio.Scanner, vals ...*int) {
	for i := range vals {
		s.Scan()
		n, _ := strconv.Atoi(s.Text())
		*vals[i] = n
	}
}

func scanIntSlice(s *bufio.Scanner, n int) []int {
	vals := make([]int, n)
	for i := range vals {
		s.Scan()
		m, _ := strconv.Atoi(s.Text())
		vals[i] = m
	}
	return vals
}