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: Accepted)

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


  def calcMinDist(n: Int, k: Int, xs: Seq[Int]): Int = {
    import scala.math._
    // 左右に行ったり来たりせず、折り返しは最大一回までにするのが最短経路になる。   
    // N本のうち連続するK本のろうそくを選ぶ方法は、"N - K + 1"通りなので、
    // 全てのパターンに対して経路を計算して、最小値を探す。
    // 経路の一番左の座標をxl, 一番右の座標をxrとすると、
    // 左 -> 右の順に訪れる場合は: |xl| + |xr - xl|
    // 右 -> 左の順に訪れる場合は: |xr| + |xr - xl|
    // が最小値となる。
    List.range(0, n-k+1).foldLeft(Int.MaxValue){(acc, l) =>
        val r = l + k - 1
        min(acc, abs(xs(r) - xs(l)) + min(abs(xs(l)), abs(xs(r))))
      }
  }

  println(calcMinDist(n, k, positions))
}