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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
// C
fscanf(STDIN, '%d %d', $n, $k);
$x = array_map('intval', explode(' ', trim(fgets(STDIN))));
if ($x[0] > 0) {
    echo $x[$k - 1];
    exit;
}
if ($x[$n - 1] < 0) {
    echo -$x[$n - $k];
    exit;
}
$l = $r = [0];
for ($i = 0; $i < $n; $i++) {
    if ($x[$i] < 0) {
        $l[] = -$x[$i];
    } elseif ($x[$i] > 0) {
        $r[] = $x[$i];
    } else {
        $k--;
    }
}
$ans = 10 ** 10;
sort($l);
for ($i = 0; $i <= $k; $i++) {
    if (!isset($l[$i]) || !isset($r[$k - $i])) continue;
    $d = [$l[$i], $r[$k - $i]];
    sort($d);
    $ans = min($ans, $d[0] * 2 + $d[1]);
}
echo $ans;