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 qualified Data.ByteString.Char8 as BC
import Data.Maybe
import qualified Data.IntMap as IM

type Map = IM.IntMap Int

readIntsLine :: IO [Int]
readIntsLine = map (fst . fromJust . BC.readInt) . BC.words <$> BC.getLine

solve :: Int -> Int -> Map -> [Int]
solve (-1) _ _ = []
solve n k m = min r1 r2 : solve (n - 1) k m
  where l = fromJust $ IM.lookup n m
        r = fromJust $ IM.lookup (n + k - 1) m
        r1 = abs l + abs (r - l)
        r2 = abs r + abs (r - l)

main :: IO ()
main = do
  [n, k] <- readIntsLine
  xs <- IM.fromList . zip [0..] <$> readIntsLine
  print . minimum $ solve (n - k) k xs