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

fscanf(STDIN, "%d %d", $n, $k);
$X = array_map('intval', explode(' ', trim(fgets(STDIN))));
const X_MAX = 100000005;
$X[] = -1 * X_MAX;
$X[] = X_MAX;
sort($X);

$l = 0;
$r = count($X);
while ($r - $l >= 1) {
    $mid = intdiv($r + $l, 2);
    if ($X[$mid] > 0) {
        $r = $mid;
    } else {
        $l = $mid + 1;
    }
}
$start = $r;

$ans = PHP_INT_MAX;
$r = 1;
for ($l = 1; $l <= $n; ++$l) {
    while ($r <= $n && $r - $l < $k) {
        ++$r;
    }
    if ($r - $l !== $k) break;

    // 左端 $l; 右端 $r - 1;
    if ($X[$l] < 0 && $X[$r - 1] > 0) {
        // -+
        $ans = min($ans, abs(2 * $X[$l]) + $X[$r - 1]);
        $ans = min($ans, abs($X[$l]) + 2 * $X[$r - 1]);
    } else {

        if (!($X[$l - 1] < 0) || !($X[$r] > 0)) continue;

        /* echo "l: $l, r: $r, start: $start", PHP_EOL; */

        // --
        // ++
        if ($X[$r - 1] >= 0) {
            $ans = min($ans, $X[$r - 1]);
        } else {
            $ans = min($ans, abs($X[$l]));
        }
    }
}

echo $ans, PHP_EOL;