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.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<$>getLine::IO[Int]
    xs<-unfoldr (B.readInt.B.dropWhile(==' '))<$>B.getLine
    --
    print $ minimum $ if elem 0 xs then solve (k-1) (filter (/=0) xs) else solve k xs
--
solve 0 _ = [0]
solve k xs@(x:_)
    | x > 0 = [xs !! (k-1)]
    | la < 0 = [negate $ (reverse xs) !! (k-1)]
    | True = solve' k xs (drop (k-1) xs)
    where la = last xs

solve' _ _ [] = []
solve' k (l:ls) (r:rs)
    | r<0 = (solve' k ls rs)
    | l>0 = []
    | True = (min (r*2-l) (r-l*2) ) : (solve' k ls rs)