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)

# 32bit整数
INT_MAX = 2147483647
UINT_MAX = 4294967295
# 64bit整数
LONGLONG_MAX = 9223372036854775807
ULONGLONG_MAX = 18446744073709551615

class Solver
  def main
    n, k = gets.split.map(&:to_i)

    # 区間（キャンドル本数）固定して全探索
    min_dist = ULONGLONG_MAX
    candles = gets.split.map(&:to_i)
    (k-1).upto(n-1) do |i|
      r_pos = candles[i]
      l_pos = candles[i - (k - 1)]
      r_dist = r_pos.abs
      l_dist = l_pos.abs

      if r_pos <= 0
        # 全部負の位置
        min_dist = l_dist if l_dist < min_dist
      elsif 0 <= l_pos
        # 全部正の位置
        min_dist = r_dist if r_dist < min_dist
      else
        # 0またぎ
        if 0 < r_pos + l_pos
          # 右のほうが遠い
          d = l_dist * 2 + r_dist
        else
          # 左のほうが遠い
          d = r_dist * 2 + l_dist
        end
        min_dist = d if d < min_dist
      end
    end

    puts min_dist
  end
end

if __FILE__ == $0
  Solver.new.main
end