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)

use std::io::prelude::*;

fn input<T: std::str::FromStr>() -> T {
    let stdin = std::io::stdin();
    let token: String = stdin
        .lock()
        .bytes()
        .map(|c| c.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().unwrap()
}

fn main() {
    let n: usize = input();
    let k: usize = input();
    let x: Vec<i64> = (0..n).map(|_| input()).collect();

    let left = x.lower_bound(&0);
    let mut ans = i64::max_value();
    if left >= k {
        ans = std::cmp::min(ans, i64::abs(x[left - k]));
    }
    if n - left >= k {
        ans = std::cmp::min(ans, x[left + k - 1]);
    }
    for i in 1..left + 1 {
        if i >= k || k - i > n - left {
            continue;
        }
        let j = k - i;
        let temp = i64::abs(x[left - i]) * 2 + x[left + j - 1];
        ans = std::cmp::min(ans, temp);
        let temp = x[left + j - 1] * 2 + i64::abs(x[left - i]);
        ans = std::cmp::min(ans, temp);
    }

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

trait LowerBound<T: Ord> {
    fn lower_bound_by<F: FnMut(&T) -> std::cmp::Ordering>(&self, f: F) -> usize;
    fn lower_bound(&self, x: &T) -> usize {
        self.lower_bound_by(|e| e.cmp(x))
    }
    fn lower_bound_by_key<U: Ord, F: FnMut(&T) -> U>(&self, x: &U, mut f: F) -> usize {
        self.lower_bound_by(|e| f(e).cmp(x))
    }
}
impl<T: Ord> LowerBound<T> for [T] {
    fn lower_bound_by<F: FnMut(&T) -> std::cmp::Ordering>(&self, mut f: F) -> usize {
        let mut l = -1 as i64;
        let mut r = self.len() as i64;
        while r - l > 1 {
            let m = ((l + r) / 2) as usize;
            if f(&self[m]) == std::cmp::Ordering::Less {
                l = m as i64;
            } else {
                r = m as i64;
            }
        }
        r as usize
    }
}