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: Time Limit Exceeded)

object Main{
  def main(args: Array[String]): Unit = {
    //n <- 本数  k <- 火をつける数
    val Seq(n, k) : Seq[Int] = io.StdIn.readLine().split(' ').map(_.toInt).toList
    val candles : Seq[Int] = io.StdIn.readLine().split(' ').map(_.toInt).toList
    println(sunukeSetFire(n,k,candles))
  }

  def sunukeSetFire(n:Int, k:Int, candles:Seq[Int]):Int ={

    val (l,r) = aaaaa(candles)

    var distances : List[Int] = Nil

    var index = 0
    while(index + k <= candles.length){

      //List(index)からList(index+k)までのリストを作る
      var list :List[Int] = Nil
      var index2 = index
      while(index2 < index + k){
        list = candles(index2) :: list
        index2 += 1
      }
      if(list.exists(i=> i==l || i == r)){
        distances = calcDistance(list.reverse) :: distances
      }
      index += 1
    }
    distances.min
  }

  def calcDistance(list: List[Int]) : Int = {
    var distance = 0
    val (nega, posi) = list.span(_ <= 0)
    if(nega.isEmpty) return posi.max
    if(posi.isEmpty) return nega.min * (-1)
    if(nega.min*(-1) < posi.max) (nega.min*(-1))*2 + posi.max
    else nega.min*(-1) + (posi.max)*2
  }

  def aaaaa(candle: Seq[Int]) ={
    val (nega, posi) = candle.span(_ <= 0)
    (if(nega.nonEmpty)nega.reverse.head else posi.head,
      if(posi.nonEmpty)posi.head else nega.reverse.head)
  }
}