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: Wrong Answer)

object Main {
  def main(args: Array[String]) {
    var points = Array[Int]()
    var count = 0
    for(line <- io.Source.stdin.getLines()) {
      val temp_point = line.split(' ').map{_.toInt}
      if(count == 0) {
        points = points :+ temp_point(1)
      }
      else {
        for(c <- temp_point) {
          points = points :+ c
        }
      }
      count += 1
    }
    
    var step = 99999999
    var first_check = true
    for(i <- 1 to points.length - 1) {
      val diff = (points(i) - points(i - 1)).abs
      if(first_check) {
        if(step > diff) {
          step = diff
        }
        first_check = false
      }
      else {
        val temp_gcd = gcd(diff, step)
        if(step > temp_gcd) {
          step = temp_gcd
        }
      }
    }

    println(step)
  }

  def gcd(a: Int, b: Int): Int = {
    if (b == 0) {
      a
    }
    else {
      gcd(b, a%b)
    } 
  }
}