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 LuaJIT (2.0.4) (judge verdict: Accepted)

local n, k = io.read("*n", "*n")
local left, right = {}, {}
for i = 1, n do
  local d = io.read("*n")
  if(d == 0) then k = k - 1
  elseif(0 < d) then table.insert(right, d)
  else table.insert(left, -d) end
end
table.sort(left)
table.sort(right)
local leftusemin = math.max(0, k - #right)
local leftusemax = math.min(k, #left)

local minlen = 0
for leftuse = leftusemin, leftusemax do
  local rightuse = k - leftuse
  local leftlen, rightlen = 0, 0
  if(0 < leftuse) then leftlen = left[leftuse] end
  if(0 < rightuse) then rightlen = right[rightuse] end
  local curlen = leftlen + rightlen + math.min(leftlen, rightlen)
  if(minlen == 0) then minlen = curlen else minlen = math.min(minlen, curlen) end
end
print(minlen)