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)

import java.io.{InputStream, OutputStream, PrintStream}
import java.util.Scanner

import scala.annotation.tailrec

object Main {

  def main(args: Array[String]): Unit = {
    val solver = new Solver(System.in, System.out)
    solver.solve()
  }

  class Solver(in: InputStream, out: OutputStream) {
    lazy val input = new Scanner(in)

    lazy val output = new PrintStream(out)

    def solve(): Unit = {
      val Array(n, k) = input.nextLine().split(" ").map(_.toInt)
      val xs = input.nextLine().split(" ").map(_.toInt)

      output.println(solve(xs.toSet, k))
    }

    def solve(xs: Set[Int], k: Int): Int = {
      var leftPos = 0
      var rightPos = 0
      var foundCount = 0

      if (xs(0)) {
        foundCount += 1
      }

      if (foundCount >= k) {
        return 0
      }

      1.to(Math.pow(10, 8).toInt).foreach { i =>
        if (xs(i)) {
          rightPos = i
          foundCount += 1
        }

        if (foundCount >= k) {
          val min = leftPos.min(rightPos)
          val max = leftPos.max(rightPos)
          return  min * 2 + max
        }

        if (xs(i * -1)) {
          leftPos = i
          foundCount += 1
        }

        if (foundCount >= k) {
          val min = leftPos.min(rightPos)
          val max = leftPos.max(rightPos)
          return  min * 2 + max
        }
      }

      0
    }

    @tailrec
    final def gcd(m: Int, n: Int): Int = {
      val (x, y) = if (m > n) (m, n) else (n, m)
      if (y != 0) gcd(y, x % y)
      else x
    }

  }

}