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.Vector.Unboxed as V
import qualified Data.ByteString.Char8 as B

solve :: Int -> Int -> V.Vector Int -> Int
solve n k xs = (\t -> if null t then 0 else minimum t) $ map (\i -> dist (xs V.! i) (xs V.! (i+k-1))) [0..n-k] where
  dist x y =
    let
      l = max (-x) 0
      r = max y 0
    in
      l + r + min l r

readInt :: B.ByteString -> Int
readInt = fst . (\(Just x) -> x) . B.readInt

main = do
  [n,k] <- map readInt . B.words <$> B.getLine
  xs <- map readInt . B.words <$> B.getLine
  print $ solve n k $ V.fromList xs