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: Wrong Answer)

n,k = gets.chomp.split(" ").map(&:to_i)
x = gets.chomp.split(" ").map(&:to_i)

def greed(query)
  if query.min >=0
    return query.max
  end

  if query.max <= 0
    return query.min
  end

  return [query.max,query.min.abs].min * 2 + [query.max,query.min.abs].max
end


now = 0
x.each_with_index do |x,idx|
  if x >= 0
    now = idx
    break
  end
end

count = []
start = [now - k,0].max
loop do
  if start > now || start + k > n
    break
  end
  query = x[start...start+k]
  count << greed(query)
  start += 1
end

puts count.min