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 Pascal (FPC 2.6.2) (judge verdict: Accepted)

var n,k,i,aa:longint;
min,count:int64;
a:array[0..100010]of longint;
function m(x,y:int64):int64;
begin 
	if x<y then exit(x)
		else exit(y);
end;
begin 
	readln(n,k);
	aa:=0;
	min:=maxlongint;
	for i:=1 to n do 
	begin
		read(a[i]);
		if a[i]<=0 then 
		begin 
			a[i]:=-a[i];aa:=i;
		end;
	end;
	if aa>=k then min:=m(min,a[aa-k+1]);
	if n-aa>=k then min:=m(min,a[aa+k]);
	for i:=0 to m(n-aa,k) do 
		if (aa>=k-i) then
		begin 
			if a[aa-k+i+1]>a[aa+i] then count:=a[aa-k+i+1]+2*a[aa+i]
				else count:=2*a[aa-k+i+1]+a[aa+i];
			min:=m(min,count);
		end;
	write(min);
end.