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 OCaml (4.02.3) (judge verdict: Wrong Answer)

let rec firstNth list n = match list with
  | [] -> []
  | _ when n = 0 -> []
  | x::rest -> x::(firstNth rest (n-1))
  

let solve n k list =
  let dists = List.map (fun x -> (x, abs x)) list in
  let sorted = firstNth (List.sort (fun x y -> if (snd x) < (snd y) then -1 else 1) dists) k in
  let maxL = List.fold_left (fun acc x -> max acc (fst x)) 0 sorted and
      minL = List.fold_left (fun acc x -> min acc (fst x)) 0 sorted in
  maxL - (min minL 0) + (min maxL (abs (min minL 0)))

let read_list_of_int () =
  let rec read_list_of_int_inner lst =
    try let ans = (Scanf.scanf "%d " (fun x->x)) in
        read_list_of_int_inner (ans::lst)
    with End_of_file ->
      List.rev lst
  in
  read_list_of_int_inner []

let () =
  let n, k = (Scanf.scanf "%d %d\n" (fun x y -> x,y)) in
  let list = read_list_of_int () in
  let ans = solve n k list in
  Printf.printf "%d\n" ans;
;;