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)
x = gets.chomp.split(" ").map(&:to_i)
minus = x.select{|x| x < 0}.reverse
plus = x.select{|x| x >= 0}
if minus.length == n
  puts -x[-k]
elsif plus.length == n
  puts x[k-1]
else
  i = plus.length >= k ? k-1 : plus.length-1
  j = k-i-2
  time = j == -1 ? plus[i] : plus[i] - minus[j]
  min_time = time
  if j != -1
    min_time = plus[i] < -minus[j] ? time + plus[i] : time - minus[j]
  end
  i -= 1
  j += 1
  while i != -2 && j <= minus.length-1
    time -= plus[i+1]
    time += plus[i] if i != -1
    time -= minus[j]
    time += minus[j-1] if j != 0
    min_time = [plus[i] < -minus[j] ? time + plus[i] : time - minus[j],min_time].min
    min_time = time if min_time > time && i == -1
    i -= 1
    j += 1
  end
  puts min_time
end