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, fastout};
use std::cmp::min;

macro_rules! echo {
  ($val:expr) => {
    println!("{}", $val);
  }
}

#[fastout]
fn main() {
  input!{
    n: usize,
    k: usize,
    mut xa: [i32; n]
  };
  let ans = match xa.iter().position(|&x| x > 0) {
    None => {
      xa[n-k] * -1
    },
    Some(mid) => {
      let mut ans = std::i32::MAX;
      xa.insert(mid, 0);
      for i in 0..=k {
        if mid >= k-i && mid+i <= n {
          let cost = min(xa[mid + i] * 2 + xa[mid-(k-i)]*-1, xa[mid+i] + xa[mid-(k-i)] * -2);
          // dbg!(i, cost);
          ans = min(ans, cost);
        }
      }
      ans
    }
  };
  echo!(ans);
}