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: Accepted)

using System;
using System.IO;
using System.Linq;
using System.Collections.Generic;
using System.Text;

public class Program
{

    public void Proc()
    {
        int[] inpt = Reader.ReadLine().Split(' ').Select(a => int.Parse(a)).ToArray();


        this.CandleCount = inpt[0];
        this.FireCount = inpt[1];

        this.Candles = Reader.ReadLine().Split(' ').Select(a => long.Parse(a)).ToArray();

        this.Dist = new long[this.CandleCount];

        this.Dist[0] = 0;
        for (int i = 1; i < this.CandleCount; i++)
        {
            this.Dist[i] = this.Dist[0] + (this.Candles[i] - this.Candles[i - 1]);
        }

        long ans = long.MaxValue;
        for (int i = 0; i < this.CandleCount; i++)
        {
            int stIdx = i;
            int edIdx = i + FireCount - 1;
            if (edIdx >= this.CandleCount)
            {
                break;
            }
            long mv = Math.Min(Math.Abs(this.Candles[edIdx]), Math.Abs(this.Candles[stIdx]));
            mv += this.Candles[edIdx] - this.Candles[stIdx];
            ans = Math.Min(mv, ans);
        }
        Console.WriteLine(ans);

    }


    long[] Dist;

    long[] Candles;

    int CandleCount;
    int FireCount;


    public class Reader
    {
        static StringReader sr;
        public static bool IsDebug = false;
        public static string ReadLine()
        {
            if (IsDebug)
            {
                if (sr == null)
                {
                    sr = new StringReader(InputText.Trim());
                }
                return sr.ReadLine();
            }
            else
            {
                return Console.ReadLine();
            }
        }
        private static string InputText = @"



5 3
-30 -10 10 20 50



";
    }

    public static void Main(string[] args)
    {
#if DEBUG
        Reader.IsDebug = true;
#endif
        Program prg = new Program();
        prg.Proc();
    }
}