Problem:
Score : 300 points

Problem Statement

There are N candles placed on a number line.
The i-th candle from the left is placed on coordinate x_i.
Here, x_1 < x_2 < ... < x_N holds.

Initially, no candles are burning.
Snuke decides to light K of the N candles.

Now, he is at coordinate 0.
He can move left and right along the line with speed 1.
He can also light a candle when he is at the same position as the candle, in negligible time.

Find the minimum time required to light K candles.

Constraints

1 \leq N \leq 10^5

1 \leq K \leq N

x_i is an integer.

|x_i| \leq 10^8

x_1 < x_2 < ... < x_N

Input

Input is given from Standard Input in the following format:

N K
x_1 x_2 ... x_N

Output

Print the minimum time required to light K candles.

Sample Input 1

5 3
-30 -10 10 20 50

Sample Output 1

40

He should move and light candles as follows:

Move from coordinate 0 to -10.

Light the second candle from the left.

Move from coordinate -10 to 10.

Light the third candle from the left.

Move from coordinate 10 to 20.

Light the fourth candle from the left.

Sample Input 2

3 2
10 20 30

Sample Output 2

20

Sample Input 3

1 1
0

Sample Output 3

0

There may be a candle placed at coordinate 0.

Sample Input 4

8 5
-9 -7 -4 -3 1 2 3 4

Sample Output 4

10

Solution in Scala (2.11.7) (judge verdict: Runtime Error)

object Main extends App {
  val Array(_, numFires) = io.StdIn.readLine().split(' ').map(_.toInt)
  val candles = io.StdIn.readLine().split(' ').map(_.toInt)

  val distanceCounter = new DistanceCounter
  println(distanceCounter.countMinDistance(candles, numFires))
}


class DistanceCounter {
  
  def countMinDistance(candlePositions: Seq[Int], numFires: Int): Int = {
    var negatives: List[Int] = Nil
    var positives: List[Int] = Nil

    for(position <- candlePositions) {
      if (position < 0) negatives = position :: negatives
      else positives = position :: positives
    }
    positives = positives.reverse

    return minDistance(Nil, negatives, positives, numFires)

  }

  /**
    * 最小ルートを計算して返却
    * 末尾再帰になっていないので、大量データだとStackOverFlowが発生する。
    *
    */
  private def minDistance(routes: List[Int], negatives: Seq[Int], positives: Seq[Int], numFires: Int): Int = {
    // 火をつけたろうそくの数が要求と一致したら、距離を計算する
    if(routes.length == numFires) calcDistance(routes.reverse)
    else
      // 現在の一から右か左に行くパターンがあるので、それぞれのルートを辿る。
      // 終端まで行ったルートに関してはハズレなので、Intの最大値を返すことで正解ルートでないことを表す。
      Math.min(
        if (negatives.isEmpty) Int.MaxValue else minDistance(negatives.head :: routes , negatives.tail , positives      , numFires) ,
        if (positives.isEmpty) Int.MaxValue else minDistance(positives.head :: routes , negatives      , positives.tail , numFires) 
        )
  }

  /**
    * 指定されたルートを通った時の距離を算出する
    */
  private def calcDistance(routes: Seq[Int]): Int = {
    var currentPosition = 0
    var distance = 0
    for(position <- routes) {
      distance = distance + Math.abs(position - currentPosition)
      currentPosition = position
    }
    distance
  }

}