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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.Scanner;
import java.util.stream.IntStream;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int N = sc.nextInt();
        int K = sc.nextInt();
        int[] x = new int[N];
        for (int i = 0; i < x.length; ++i) {
            x[i] = sc.nextInt();
        }

        System.out.println(solve(x, K));

        sc.close();
    }

    static int solve(int[] x, int K) {
        int middleIndex = 0;
        while (middleIndex != x.length && x[middleIndex] < 0) {
            ++middleIndex;
        }

        int middleIndex_ = middleIndex;
        int[] leftDistances = IntStream.range(0, middleIndex).map(i -> -x[middleIndex_ - 1 - i]).toArray();
        int[] rightDistances = IntStream.range(0, x.length - middleIndex).map(i -> x[middleIndex_ + i]).toArray();

        return Math.min(computeMinTime(K, leftDistances, rightDistances),
                computeMinTime(K, rightDistances, leftDistances));
    }

    static int computeMinTime(int K, int[] firstDistances, int[] secondDistances) {
        int result = Integer.MAX_VALUE;
        for (int i = 0; i < firstDistances.length && i < K; ++i) {
            if (i == K - 1) {
                result = Math.min(result, firstDistances[i]);
            } else if (secondDistances.length >= K - i - 1) {
                result = Math.min(result, firstDistances[i] * 2 + secondDistances[K - i - 2]);
            }
        }

        return result;
    }
}