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)

neg = []
pos = []

x.each do |e|
  if e < 0
    neg << e.abs
  else
    pos << e
  end
end

neg.reverse!

if neg.empty?
  puts pos[k - 1]
elsif pos.empty?
  puts neg[k - 1]
else
  ans = []
  0.upto(k) do |i|
    next if i > neg.length || k - i > pos.length
    tm = 0
    left = neg[i - 1]
    right = pos[k - i - 1]
    p [left, right]
    tm = left + right + [left, right].min
    ans << tm
  end
  puts ans.min
end