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: Accepted)

    fn read1<T: std::str::FromStr>() -> T {
        let mut s = String::new();
        std::io::stdin().read_line(&mut s).ok();
        s.trim().parse().ok().unwrap()
    }
     
    pub fn readn<T: std::str::FromStr>(delimiter: &str) -> Vec<T> {
        let s = read1::<String>();
        s.split(delimiter).map(|e| e.parse().ok().unwrap()).collect::<Vec<T>>()
    }
     
    fn main() {
        let nk = readn::<usize>(" ");
        let mut n = nk[0];
        let mut k = nk[1];
     
        let mut x = readn::<isize>(" ");
        let zero = match x.binary_search(&0) {
            Ok(p) => {
                k -= 1;
                p
            },
            Err(p) => {
                x.insert(p, 0);
                n += 1;
                p
            }
        };
        let mut l = (0..zero).rev().map(|i| -x[i] as usize).collect::<Vec<usize>>();
        let mut r = (zero+1..n).map(|i| x[i] as usize).collect::<Vec<usize>>();
        l.insert(0, 0);
        r.insert(0, 0);
        
        let minr = if k < zero {
            0
        } else {
            k - zero
        };
        let maxr = if k < n - zero - 1 {
            k
        } else {
            n - zero - 1
        };
     
        let mut ans = 1_000_000_000;
        for i in minr..maxr+1 {
            ans = std::cmp::min(std::cmp::min(r[i] + 2 * l[k-i], 2 * r[i] + l[k-i]), ans);
        }
     
        println!("{}", ans);
    }