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 Rust (1.42.0) (judge verdict: Accepted)

use proconio::input;
use std::cmp::min;

fn main() {
    input! {
        n: usize,
        k: usize,
        xx: [i64; n],
    }

    let mut positives = vec![];
    let mut negatives = vec![];
    let mut zero = None;

    for x in xx {
        match x {
            0 => zero = Some(0),
            x if x > 0 => positives.push(x),
            x if x < 0 => negatives.push(-x),
            _ => unreachable!(),
        }
    }

    negatives.reverse();

    let mut count_pos = min(k, positives.len());

    let mut count_neg = if k > positives.len() { k - positives.len() } else { 0 };

    if zero.is_some() {
        if count_pos > 0 {
            count_pos -= 1;
        }
        if count_neg > 0 {
            count_neg -= 1;
        }
    }

    let mut ans = std::i64::MAX;

    for _ in 0..k {
        let pos = if count_pos > 0 {
            positives[count_pos-1]
        } else {
            0
        };
        let neg = if count_neg > 0 {
            if count_neg > negatives.len() {
                break;
            }
            negatives[count_neg-1]
        } else {
            0
        };
        ans = min(ans, pos * 2 + neg);
        ans = min(ans, pos + neg * 2);

        if count_pos == 0 {
            break;
        }
        count_pos -= 1;
        count_neg += 1;
    }

    println!("{}", ans);
}