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.

5 3
-30 -10 10 20 50

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.

3 2
10 20 30

20

1 1
0

0

• There may be a candle placed at coordinate $0$.

8 5
-9 -7 -4 -3 1 2 3 4

10