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)

// by syu
package main

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

var in = NewScanner(os.Stdin, 0)

func main() {
	N, X := in.Int(), in.Int()
	x := in.ArrayInt(N)
	x = append(x, X)
	sort.Ints(x)
	ans := x[1] - x[0]
	for i := 0; i < len(x)-1; i++ {
		gcd := Gcd(ans, x[i+1]-x[i])
		if gcd < ans {
			ans = gcd
		}
	}
	Pln(ans)
}

type Scanner struct {
	*bufio.Scanner
}

func NewScanner(r io.Reader, max int) *Scanner {
	s := bufio.NewScanner(r)
	s.Split(bufio.ScanWords)
	if max <= 0 {
		max = 1048576
	}
	s.Buffer([]byte{}, max)
	return &Scanner{s}
}
func (s *Scanner) Int() int {
	s.Scan()
	i, e := strconv.ParseInt(s.Text(), 10, 64)
	if e != nil {
		panic(e)
	}
	return int(i)
}
func (s *Scanner) ArrayInt(n int) (r []int) {
	for i := 0; i < n; i++ {
		r = append(r, s.Int())
	}
	return
}
func Pln(s ...interface{}) {
	fmt.Println(s...)
}
func Gcd(a, b int) int {
	t := 0
	for b != 0 {
		t = a % b
		a = b
		b = t
	}
	return a
}