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: Wrong Answer)

#![allow(unused)]
use binsearch::*;
use io::*;
use std::cmp::{max, min};
use std::collections::BTreeSet;

fn main() {
    let mut buf = read_string();
    let mut sc = Scanner::new(&mut buf);

    let n: usize = sc.next();
    let mut k: usize = sc.next();
    let x: Vec<i32> = (0..n)
        .filter_map(|_| {
            let a: i32 = sc.next();
            if a == 0 {
                k -= 1;
                None
            } else {
                Some(a)
            }
        }).collect();

    if x.len() == 0 {
        println!("0");
        return;
    }

    let z = upper_bound(&x, &0);
    let p = max(0, z as i32 - k as i32) as usize;
    let q = min(n - k, z);
    let ans = (p..q + 1)
        .map(|i| {
            if i < z {
                if i + k < z {
                    x[i].abs()
                } else {
                    2 * x[i].abs() + x[i + k - 1]
                }
            } else {
                x[i + k - 1]
            }
        }).min()
        .unwrap();

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

pub mod io {
    use std;
    use std::io::Read;

    pub struct Scanner<'a> {
        iter: std::str::SplitWhitespace<'a>,
    }

    impl<'a> Scanner<'a> {
        pub fn new(buf: &'a String) -> Scanner<'a> {
            Scanner {
                iter: buf.split_whitespace(),
            }
        }

        pub fn next<T: std::str::FromStr>(&mut self) -> T {
            let s = self.iter.next().unwrap();
            s.parse().ok().expect("cannot parse string")
        }

        pub fn next_vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
            (0..n).map(|_| self.next()).collect()
        }
    }

    pub fn read_string() -> String {
        let mut buf = String::new();
        std::io::stdin().read_to_string(&mut buf).ok().unwrap();
        buf
    }

    fn read_line<T: std::str::FromStr>() -> T {
        let mut buf = String::new();
        std::io::stdin().read_line(&mut buf).unwrap();
        buf.trim().parse().ok().unwrap()
    }

    fn read_vec<T: std::str::FromStr>() -> Vec<T> {
        read_line::<String>()
            .split_whitespace()
            .map(|e| e.parse().ok().unwrap())
            .collect()
    }
}

pub mod binsearch {
    pub fn lower_bound<T: Ord>(v: &Vec<T>, value: &T) -> usize {
        let mut first = 0;
        let mut len = v.len();
        while len != 0 {
            let half = len / 2usize;
            let mut mid = first + half;
            if *value <= v[mid] {
                len = half;
            } else {
                len -= half + 1;
                mid += 1;
                first = mid;
            }
        }
        first
    }

    pub fn upper_bound<T: Ord>(v: &Vec<T>, value: &T) -> usize {
        let mut first = 0;
        let mut len = v.len();
        while len != 0 {
            let half = len / 2usize;
            let mut mid = first + half;
            if *value < v[mid] {
                len = half;
            } else {
                len -= half + 1;
                mid += 1;
                first = mid;
            }
        }
        first
    }
}