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
a=gets.split.map &:to_i
dir=[]
if a.index(0)
  pt0=a.index(0)
  k-=1
else
  n+=1
  if a[0]>0
    pt0=0
    a.insert(0,0)
  elsif a[n-1]<0
    pt0=n
    a.insert(n,0)
  else
    (n-1).times do|i|
      if a[i]<0&&a[i+1]>0
        pt0=i+1
        a.insert(i+1,0)
        break
      end
    end
  end
end
n.times do|i|
  if i<pt0
    if pt0-i==k
      dir<<(-a[i])
    elsif pt0-i<k&&k+i<n
      dir<<(-a[i]*2+a[k+i])
    end
  elsif i>pt0
    if i-pt0==k
      dir<<a[i]
    elsif i-pt0<k&&i-k>0
      dir<<a[i]*2-a[i-k]
    end
  else
    k==0&&dir<<0
  end
end
puts dir.min