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 {
  def main(args: Array[String]): Unit = {
    solve2
  }


  def solve2(): Unit = {
    val sc = new java.util.Scanner(System.in)
    val n, k = sc.nextInt
    val a = new Array[Long](n)
    for (i <- 0 until n) {
      a(i) = sc.nextLong
    }

    // 左からk個ずつとってみて、最小を求めてみる
    var ans = Long.MaxValue
    for (i <- 0 to n - k) {
      val x = a(i)
      val y = a(i + k - 1)

      val dist = math.abs(y - x)
      ans = math.min(ans, math.min((math.abs(x) + dist), (math.abs(y) + dist)))

    }
    println(ans)
  }


  // これだとTLE!!!!!
  def solve(): Unit = {
    val sc = new java.util.Scanner(System.in)
    val n, k = sc.nextInt
    val a = new Array[Long](n)
    for (i <- 0 until n) {
      a(i) = sc.nextLong
    }

    // 左からk個ずつとってみて、最小を求めてみる
    var ans = Long.MaxValue
    for (i <- 0 to n - k) {
      val part = a.slice(i, i + k)
      val min = part.min
      val max = part.max
      val (greater, lesser) = if (min.abs >= max.abs) (min.abs, max.abs) else (max.abs, min.abs)

      if ((min < 0 && max < 0) || (min > 0 && max > 0)) {
        ans = math.min(ans, greater)
      } else {
        ans = math.min(ans, greater + 2 * lesser)
      }
    }
    println(ans)
  }
}