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 (4.10.0) (judge verdict: Accepted)

Scanf.scanf "%d %d" (fun n k ->
    let x = Array.init n (fun _ -> Scanf.scanf " %d" (fun x -> x)) in

    let rec loop p acc =
        if p = n then acc else
            let s1 = x.(p - k + 1) in
            let s2 = x.(p) in
            let v1 = if s1 < 0 && s2 <= 0 then abs s1 else
                     if s1 >= 0 && s2 > 0 then s2 else
                         min (abs s1 * 2 + s2) (abs s1 + s2 * 2)
            in
            let acc = min acc v1 in
            loop (p + 1) acc
    in
    loop (k - 1) max_int |> Printf.printf "%d\n"
)