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: Runtime Error)

import scala.annotation.tailrec
import scala.collection.mutable.ArrayBuffer

object Main extends App {
  val Array(_, pointX) = io.StdIn.readLine().split(' ').map(_.toInt)
  val cities = io.StdIn.readLine().split(' ').map(_.toInt)
  val distance = new Distance
  println(distance.getD(cities, pointX))
}

class Distance {
  def getD(citiesPoint : Seq[Int], startPoint : Int): Int = {
    val distance : Seq[Int] = getPointCitiesDistance(citiesPoint, startPoint)
    calcGreatestCommonFactor(distance)
  }

  /*
   * 都市と座標Xとの距離(絶対値を求める) 距離0(座標X=都市)は含めない
   */
  private def getPointCitiesDistance(citiesPoint: Seq[Int], startPoint: Int): Seq[Int] = {
    val distanceBuffer = new ArrayBuffer[Int]

    for (point <- citiesPoint) {
      if (point != startPoint) distanceBuffer += (point - startPoint).abs
    }
    val distance = distanceBuffer.toList

    distance
  }

  /*
   * Seq内の値の最大公約数を求める
   */
  //@tailrec
  private def calcGreatestCommonFactor(distance : Seq[Int]) : Int = distance.size match {
    case 2 => calcGCF(distance.head, distance.tail.head)
    case 1 => distance.head
    case _ => calcGCF(calcGreatestCommonFactor(distance.tail), distance.head)
  }

  /*
   * 2数の最大公約数を求める
   */
  @tailrec
  private def calcGCF(a : Int, b : Int): Int = b match{
    case 0 => a
    case _ if b < a => calcGCF(b, b % a)
    case _ => calcGCF(a, a % b)
  }
}