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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Control.Applicative
import Data.ByteString.Char8 (ByteString)
import qualified Data.ByteString.Char8 as B
import Data.List
import Data.Char (isSpace)

main :: IO ()
main = solve <$> f <*> f >>= print
  where
    f = readil B.readInt <$> B.getLine

solve :: [Int] -> [Int] -> Int
solve [n, k] xs = f 1000000000 xs (drop (k-1) xs)
  where
    f t _ [] = t
    f t (y:ys) (z:zs)
      | y * z >= 0 = f (min t (max (abs y) (abs z))) ys zs
      | otherwise = f (min t (max (abs y) (abs z) + 2 * (min (abs y) (abs z)))) ys zs

readil :: Integral a =>  (ByteString -> Maybe (a, ByteString)) -> ByteString -> [a]
readil f = unfoldr g
  where
    g s = do
      (n, s') <- f s
      return (n, B.dropWhile isSpace s')