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) 
candles = Array.new
candles = gets.split.map(&:to_i) 


min_sum = 4*[candles[0].abs, candles[n-1].abs].max
#find the time to time to light k candles for every sequence of k candles
for i in 0..candles.length-k 
	if candles[i] > 0
		sum = candles[i+k-1]
	elsif candles[i+k-1] < 0
		sum = -candles[i]
	else
		if -candles[i] <= candles[i+k-1]
			sum = 2*(-candles[i]) + candles[i+k-1]
	    else
	    	sum = -candles[i] + 2*candles[i+k-1]
	    end
	end
	
	if sum < min_sum
		min_sum = sum
	end
end

puts min_sum