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 {
  import java.util.Scanner

  implicit class RichScanner(sc: Scanner) {
    def readStrings(n: Int): Array[String] = Array.fill(n) { sc.next() }
    def readInts(n: Int): Array[Int] = Array.fill(n) { sc.nextInt() }
    def readLongs(n: Int): Array[Long] = Array.fill(n) { sc.nextLong() }
    def readLineStrings: Array[String] = sc.nextLine().split(' ')
    def readLineInts: Array[Int] = readLineStrings.map(_.toInt)
    def readLineLongs: Array[Long] = readLineStrings.map(_.toLong)
  }

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

  def solve(sc: Scanner): Unit = {
    val Array(n, k) = sc.readLineInts
    val rawX = sc.readLineInts
    val zero = rawX.count(_ == 0)
    val positives = rawX.filter(_ > 0)
    val negatives = rawX.filter(_ < 0).reverse.map(_ * (-1))

    val K = k - zero

    def requiredTimes(firstDirection: Array[Int], secondDirection: Array[Int]): IndexedSeq[Option[Int]] = {
      (1 to K).map(firstShiftAmount =>
        if (firstShiftAmount > firstDirection.length) None
        else {
          val firstDirectionEdgeElement = firstDirection(firstShiftAmount - 1)
          val remaining = K - firstShiftAmount
          if (remaining == 0) {
            Some(firstDirectionEdgeElement)
          } else if(remaining > secondDirection.length) {
            None
          } else {
            val secondDirectionEdgeElement = secondDirection(remaining - 1)
            Some(2 * firstDirectionEdgeElement + secondDirectionEdgeElement)
          }
        }
      )
    }

    val answer = if (K == 0) {
      0
    } else {
      val times = requiredTimes(positives, negatives) ++ requiredTimes(negatives, positives)
      times.flatten.min
    }
    println(answer)
  }
}