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: Runtime Error)

import Control.Monad
import Data.List
import qualified Data.ByteString.Char8 as B
import qualified Data.Vector.Unboxed as V
main=do
    (n:k:_)<-map read.words<$>getLine::IO[Int]
    (ps,ms)<-partition (>=0).unfoldr (B.readInt.B.dropWhile(==' '))<$>B.getLine
    --
    print $ minimum $ solve k ps $ reverse ms
--
solve k ps [] = [ps !! (k-1)]
solve k [] ms = [negate $ ms !! (k-1)]
solve k pa@(p:ps) ms
    | p == 0 = solve' (k-1) ps ms
    | True   = solve' k pa ms
--
solve' 0 _ _ = [0]
solve' k ps ms =  (pp:) $ (mm:) $ concatMap (\i -> [f i, g i]) [max 1 k-(length ms)..min (k-1) (length ps)]
    where
        pv = V.fromList ps
        mv = V.fromList ms
        pp = (ps ++ (repeat (10^5))) !! (k-1)
        mm = negate $(ms ++ (repeat $ negate $ 10^5)) !! (k-1)
        f i = (pv V.! (i-1))*2 - (mv V.! (k-i-1))
        g i = (pv V.! (i-1)) - (mv V.! (k-i-1))*2