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: Runtime Error)

if !ENV['RUBY_THREAD_VM_STACK_SIZE']
  exec({'RUBY_THREAD_VM_STACK_SIZE'=>'1000000000'}, '/usr/bin/ruby', $0)
end
def dfs(ind, now = 0, sum = 0, cnt = 0, prev = [])
  if cnt >= K
    @ans = sum if @ans > sum
    return
  elsif @ans <= sum # 枝切り
    return
  end
  ((prev[0] || ind) - 1).downto(0) do |i|
    dfs(i, @arr[i], sum + (now - @arr[i]).abs, cnt + 1, prev.dup.unshift(i))
    break
  end
  ((prev[-1] || ind - 1) + 1).upto(N - 1) do |i|
    dfs(i, @arr[i], sum + (now - @arr[i]).abs, cnt + 1, prev.dup << i)
    break
  end
end
INF = 10**9
N, K = gets.split.map(&:to_i)
@arr = gets.split.map(&:to_i)
@ans = INF
# binding.pry
dfs(@arr.bsearch_index{|x|x >= 0})
puts @ans