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 1.8.0) (judge verdict: Accepted)

import java.util.Arrays;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        try (Scanner in = new Scanner(System.in)) {
            int N = in.nextInt();
            int K = in.nextInt();
            int[] x = new int[N + 1];
            for (int i = 0; i < N; i++) {
                x[i] = in.nextInt();
            }
            x[N] = 0;
            Arrays.sort(x);

            int index0 = 0;
            for (int i = 0; i < N + 1; i++) {
                if (x[i] == 0) {
                    index0 = i;
                    break;
                }
            }

            int min = (int) 1e9;
            for (int i = 0; i <= K; i++) {
                if (index0 - i >= 0 && index0 + (K - i) < x.length) {
                    min = Math.min(min, 2 * Math.abs(x[index0 - i]) + Math.abs(x[index0 + (K - i)]));
                }
                if (index0 - (K - i) >= 0 && index0 + i < x.length) {
                    min = Math.min(min, Math.abs(x[index0 - (K - i)]) + 2 * Math.abs(x[index0 + i]));
                }
            }

            System.out.println(min);
        }
    }
}