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 (1.15.1) (judge verdict: Runtime Error)

fn main() {
    let (_n, k) = read_tuple::<usize>();
    let mut positions: Vec<i64> = read_vec();

    positions.sort_by_key(|x| x.abs());

    let to_fire = positions.iter().take(k);
    let left = to_fire.clone().min().unwrap();
    let right = to_fire.max().unwrap();

    let mut ans = if left * right < 0 {
        let (near, far) = if left.abs() < right.abs() {
            (left.abs(), right.abs())
        } else {
            (right.abs(), left.abs())
        };
        near * 2 + far 
    } else {
        std::cmp::max(left.abs(), right.abs())
    };

    let plus_position: Vec<&i64> = positions.iter().filter(|&&x| x >= 0).collect();
    if plus_position.len() >= k && *plus_position[k-1] < ans {
        ans = *plus_position[k];
    }
    let minus_position: Vec<&i64> = positions.iter().filter(|&&x| x <= 0).collect();
    if minus_position.len() >= k && minus_position[k-1].abs() < ans {
        ans = minus_position[k].abs();
    }

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

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().split_whitespace()
        .map(|e| e.parse().ok().unwrap()).collect()
}
fn read_tuple<T: std::str::FromStr + Copy>() -> (T, T) {
    let temp = read_vec();
    (temp[0], temp[1])
}