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 Scala (2.11.7) (judge verdict: Accepted)

object Main {
  import java.util.Scanner
  import scala.annotation.tailrec

  def readStrings(n: Int)(implicit sc: Scanner): Array[String] = Array.fill(n) { sc.next() }
  def readInts(n: Int)(implicit sc: Scanner): Array[Int] = Array.fill(n) { sc.nextInt() }
  def readLongs(n: Int)(implicit sc: Scanner): Array[Long] = Array.fill(n) { sc.nextLong() }
  def readLineStrings(implicit sc: Scanner): Array[String] = sc.nextLine().split(' ')
  def readLineInts(implicit sc: Scanner): Array[Int] = readLineStrings.map(_.toInt)
  def readLineLongs(implicit sc: Scanner): Array[Long] = readLineStrings.map(_.toLong)

  def main(args: Array[String]): Unit = solve(new Scanner(System.in))

  def solve(implicit sc: Scanner): Unit = {
    @tailrec def gcd(a: Int, b: Int): Int = if (b == 0) a else gcd(b, a % b)

    val Array(n, x) = readLineInts
    val xs = readLineInts
    val sortedXs = (xs.toList :+ x).sorted
    val distances = sortedXs.zip(sortedXs.drop(1)).map(pair => pair._2 - pair._1)
    println(distances.reduce(gcd))
  }
}