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: Wrong Answer)

import Control.Monad
import Data.List
import Control.Arrow

getInts :: IO [Int]
getInts = do s <- getLine
             return $ map read $ words s

getLines :: Int -> IO [String]
getLines n = replicateM n $ getLine

solve k as bs = let ks  = take k $ sort ([ (a, True) | a <- as ] ++ [ (2 * b, False) | b <- bs ])
                    amx = foldl' max 0 [ a | (a, c) <- ks, c == True ]
                    bmx = foldl' max 0 [ b | (b, c) <- ks, c == False ]
                in amx + bmx


main = do [n, k] <- getInts
          xs <- getInts
          let as = [ -x | x <- xs, x < 0 ]
          let bs = [ x | x <- xs, x >= 0 ]
          print (solve k as bs `min` solve k bs as)