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.List
import Data.Array
import Data.Maybe
import qualified Data.ByteString.Char8 as BS

listToTuple2 [a,b] = (a,b)
readIntBS = fst . fromJust . BS.readInt

main :: IO ()
main = do
  (n,k) <- listToTuple2 . map read . words <$> getLine :: IO (Int,Int)
  xs <- map readIntBS . BS.words <$> BS.getLine :: IO [Int]

  let
    (a,b) = span (<0) xs
    a_ = listArray (0,length a) $ 0 : (reverse $ map negate a)
    b_ = listArray (0,length b) $ 0 : b

  print $ minimum [min (a_!l*2+b_!r) (a_!l+b_!r*2) | l<-[0..length a], let r=if k-l<0 then 0 else k-l, r<=length b]