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 Common Lisp (SBCL 1.1.14) (judge verdict: Runtime Error)

(let* ((n (read))
       (m (read))
       (lst (loop :repeat n :collect (read)))
       (z (loop :for k :on lst
                :for j :from 0
                :if (cdr k)
                  :if (<= (first k) 0 (second k))
                    :return (if (= 0 (first k))
                                (cons j j)
                                (cons j (1+ j))) :end
                :else :return j)))
  (princ (loop :for k :from (- (car z) (1- m)) :upto (1+ (car z))
               :for j := (+ k m)
               :if (and (<= 0 k) (<= j n))
                 :minimize (let* ((a (subseq lst k (1+ (car z))))
                                  (b (subseq lst (cdr z) j)))
                             (min (+ (* 2 (abs (car a))) (car (last b)))
                                  (+ (abs (car a)) (* 2 (car (last b)))))))))