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)
pluss, minuss = gets.chomp.split(' ').map(&:to_i).partition { |x| x >= 0 }

if pluss.first == 0
  pluss.shift
  k -= 1
end

if k == 0
  puts 0
  exit
end

N_MAX = 100_000 * 3

minuss = minuss.reverse
time = N_MAX
0.upto(k).each do |i|
  x = k - i
  front_time = N_MAX
  if (x == 0 || x < pluss.length) && (i == 0 || i < minuss.length)
    front_time = i == 0 ? 0 : minuss[i - 1].abs * 2
    front_time += x == 0 ? 0 : pluss[x - 1]
  end
  back_time = N_MAX
  if (x == 0 || x < minuss.length) && (i == 0 || i < pluss.length)
    back_time = i == 0 ? 0 : pluss[i - 1] * 2
    back_time += x == 0 ? 0 : minuss[x - 1].abs
  end
  time = [time, front_time, back_time].min
end
puts time