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)

n,k=gets.split.map(&:to_i)
if n==1
  puts (gets.to_i).abs
end
x=gets.split.map(&:to_i)
s=x.bsearch_index {|x| x>=0}
if s==nil
  x << 0
  n+=1
  k+=1
elsif x[s]>0
  x.insert(s,0)
  n+=1
  k+=1
end
a=1/0.0
[s-k+1,0].max.upto([s,n-k].min) do |i|
  t=-x[i]*2+x[i+k-1]
  if t<a
    a=t
  end
  t=-x[i]+x[i+k-1]*2
  if t<a
    a=t
  end
end
puts a