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: Accepted)

INF = 10 ** 9

n, k = gets.chomp.split(" ").map(&:to_i)
candles = gets.chomp.split(" ").map(&:to_i)

if candles.include?(0)
  k -= 1
  candles.delete(0)
end

if k == 0
  puts 0
  exit
end

minus_candles = []
plus_candles = []

candles.each do |candle|
  if candle < 0
    minus_candles << candle.abs
  else
    plus_candles << candle
  end
end

minus_candles.reverse!

([k - minus_candles.length, 0].max).times do
  minus_candles << INF
end

([k - plus_candles.length, 0].max).times do
  plus_candles << INF
end

costs = []

minus_candles.each_with_index do |minus_candle, index|
  if k - index - 2 >= 0
    costs << minus_candle + plus_candles[k - index - 2] * 2
    costs << minus_candle * 2 + plus_candles[k - index - 2]
  end
end

costs << plus_candles[k - 1]
costs << minus_candles[k - 1]

puts costs.min