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 2.0.3) (judge verdict: Accepted)

;;; body

(defun solve (n k x)
  (flet ((calc-dist (i-left i-right)
           (let ((left (aref x i-left))
                 (right (aref x (1- i-right))))
             (min (+ (abs left) (abs (- right left)))
                  (+ (abs right) (abs (- right left)))))))
    (if (= n 1)
        (abs (aref x 0))
        (reduce #'min 
                (let ((acc nil))
                  (loop with i = 0  while (<= (+ i k) n) do
                       (push (calc-dist i
                                        (+ i k))
                             acc)
                       (incf i))
                  acc)))))

(defun main ()
  (let ((n (read))
        (k (read)))
    (let ((x (make-array n
                         :initial-contents (loop repeat n collect (read)))))
      (princ (solve n k x))
      (fresh-line))))

#-swank (main)