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.split.map(&:to_i)
x = gets.split.map(&:to_i)
x.sort!
left = []
right = []
ans = []

n.times do |i|
  if x[i] < 0
    left << x[i].abs
  elsif x[i] > 0
    right << x[i]
  else
    k -= 1
  end
end
if k > 0
  left.reverse!
  if !left.empty? && left.length >= k
    ans << left[k-1]
  end

  if !right.empty? && right.length >= k
    ans << right[k-1]
  end

  if !right.empty? && !left.empty?
    i = 0
    l,r = 0
    while i < k
      if left.empty?
        r = right.shift
      elsif right.empty?
        l = left.shift
      elsif left[0] < right[0]
        l = left.shift
      else
        r = right.shift
      end
      i += 1
    end

    ans << l + r + [l,r].min
  end
end
puts k <= 0 ? 0 : ans.min