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 (2.7.1) (judge verdict: Accepted)

n, k = gets.chomp.split.map(&:to_i)
@nega_candles = []
@posi_candles = []
gets.chomp.split.each do |candle|
  if candle.to_i  <= 0
    @nega_candles.push candle.to_i
  else
    @posi_candles.push candle.to_i
  end
end

# 0から近い順にしておく
@nega_candles.reverse!

cal_distance = lambda do |l, r|
  left = l.zero? ? 0 : @nega_candles[l - 1]
  right = r.zero? ? 0 : @posi_candles[r - 1]
  [2 * right - left, right - 2 * left ].min
end

ans = Float::INFINITY
(k + 1).times do |i|
  l = i
  r = k - i
  next if r > @posi_candles.size
  break if l > @nega_candles.size
  ans = [ans, cal_distance.(l, r)].min
end

puts ans