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)

n,k = gets.split.map &:to_i
x = gets.split.map &:to_i

minus = x.select{|i|i < 0}.reverse
plus = x.select{|i|i >= 0}

result = 1e9

#左に行くだけ
if minus.size >= k
    result = -minus[k-1]
end

#右に行くだけ
if plus.size >= k
    result = [result, plus[k-1]].min
end

#左に行ってから右に行く
(0..(minus.size)).each do |i|
    if minus[i] && plus[k-i-2]
        temp = 0
        temp -= minus[i] * 2
        temp += plus[k-i-2]
        if temp <= result
            result = temp
        end
    end
end

#右に行ってから左に行く
(0..(plus.size)).each do |i|
    if plus[i] && minus[k-i-2]
        temp = 0
        temp += plus[i] * 2
        temp -= minus[k-i-2]
        if temp <= result
            result = temp
        end
    end
end

puts result