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.

Examples

Input

5 3
-30 -10 10 20 50

Output

40

Input

3 2
10 20 30

Output

20

Input

1 1
0

Output

0

Input

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

Output

10

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