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 C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;

namespace AtCoder
{
	public class Program
	{
		// ABC107-C
		static void Main(string[] args)
		{
			string[] vs = Console.ReadLine().Split();
			int N = int.Parse(vs[0]);
			int K = int.Parse(vs[1]);
			vs = Console.ReadLine().Split();
			int[] candle = new int[N];
			for (int i = 0; i < N; i++) {
				candle[i] = int.Parse(vs[i]);
			}
			int min = 0, max = K - 1;
			int time = 0;
			do {
				int tmp;
				tmp = Math.Min(Math.Abs(candle[min]), Math.Abs(candle[max]));
				for (int i = min; i < max; i++) {
					tmp += Math.Abs(candle[i + 1] - candle[i]);
				}
				if (time == 0 || time > tmp) {
					time = tmp;
				}
				min++;
				max++;
			} while (max < N);
			Console.WriteLine(time);
		}
	}
}