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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

n, k = gets.split.map(&:to_i)
xn = gets.split.map(&:to_i)
ans = (10**8) * (10**5)

unless xn.include?(0)
  xn.push(0).sort!
  k += 1
  n += 1
end

pos = xn.index(0)
left = [0, pos-k+1].max
right = [n-1, pos+k-1].min
xn = xn[left..right]

if n == k
  # right -> left
  score = xn[-1] * 2 + xn[0].abs
  ans = score if ans > score
  # left -> right
  score = xn[-1] + xn[0].abs * 2
  ans = score if ans > score
else
  (n-k).times do |i|
    scope = xn[i...(k+i)]
    num = scope.select{|d| d < 0 }.size
    if num == k or num == 0
      score = scope.map{|s| s.abs }.max
      ans = score if ans > score
    else
      # right -> left
      score = scope[-1] * 2 + scope[0].abs
      ans = score if ans > score
      # left -> right
      score = scope[-1] + scope[0].abs * 2
      ans = score if ans > score
    end
  end
end
puts ans