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 java.util.Scanner

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

  def solve(in: String): String = solve(new Scanner(in))

  def gcd(seq: Seq[Int]): Int = {
    require(seq.nonEmpty)
    gcd(seq.head, seq.tail: _*)
  }

  def gcd(m: Int, ns: Int*): Int = m match {
    case 1 => m
    case _ =>
      ns match {
        case Nil => m.abs
        case n +: rest => gcd(gcd(m, n), rest: _*)
      }
  }

  def solve(sc: Scanner): String = {
    val N = sc.nextInt
    val X = sc.nextInt
    val x = (Array.fill(N)(sc.nextInt) :+ X).sorted

    val xd = for (i <- 1 to N) yield x(i) - x(i - 1)
    val result = gcd(xd)

    result.toString
  }
}