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.Text;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using static System.Console;
using static System.Math;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            new Program().Solve(new ConsoleInput(Console.In, ' '));
#if DEBUG
            ReadLine();
#endif
        }

        void Solve(ConsoleInput cin)
        {
            int n = cin.ReadInt;
            int k = cin.ReadInt;
            long[] a_n = cin.ReadLongArray(n);

            int mIndex = BinarySearch(a_n, 0);
            if (mIndex < 0)
            {
                Console.WriteLine(Abs(a_n[k - 1]));
            }
            else if (mIndex == n - 1)
            {
                Console.WriteLine(Abs(a_n[n - k]));
            }
            else
            {
                //rl
                long ans = long.MaxValue;
                for (int i = 1; i <= k; i++)
                {
                    if (mIndex + i >= n)
                    {
                        break;
                    }

                    if (mIndex - (k - i) < 0)
                    {
                        continue;
                    }

                    ans = Min(2 * Abs(a_n[mIndex + i]) + Abs(a_n[mIndex - (k - i - 1)]), ans);
                }
                //lr
                for (int i = 1; i <= k; i++)
                {
                    if (mIndex + 1 - i < 0)
                    {
                        break;
                    }

                    if (mIndex + k - i >= n)
                    {
                        continue;
                    }

                    ans = Min(Abs(a_n[mIndex + k - i]) + 2 * Abs(a_n[mIndex + 1 - i]), ans);
                }
                Console.WriteLine(ans);
            }
        }

        static int BinarySearch(long[] array, long val)
        {
            int bottom = 0;
            int top = array.Length;

            while (bottom + 1 < top)
            {
                int mid = (bottom + top) / 2;
                if (array[mid] <= val)
                {
                    bottom = mid;
                }
                else
                {
                    top = mid;
                }
            }
            if (bottom == 0 && val < array[bottom]) return -1;
            else return bottom;
        }

        class ConsoleInput
        {
            private readonly System.IO.TextReader _stream;
            private char _separator = ' ';
            private Queue<string> inputStream;

            public ConsoleInput(System.IO.TextReader stream, char separator = ' ')
            {
                this._separator = separator;
                this._stream = stream;
                inputStream = new Queue<string>();
            }

            public string Read
            {
                get
                {
                    if (inputStream.Count != 0) return inputStream.Dequeue();
                    string[] tmp = _stream.ReadLine().Split(_separator);
                    for (int i = 0; i < tmp.Length; ++i)
                        inputStream.Enqueue(tmp[i]);
                    return inputStream.Dequeue();
                }
            }

            public string ReadLine { get { return _stream.ReadLine(); } }
            public int ReadInt { get { return int.Parse(Read); } }
            public long ReadLong { get { return long.Parse(Read); } }
            public double ReadDouble { get { return double.Parse(Read); } }
            public string[] ReadStrArray(long N) { var ret = new string[N]; for (long i = 0; i < N; ++i) ret[i] = Read; return ret; }
            public int[] ReadIntArray(long N) { var ret = new int[N]; for (long i = 0; i < N; ++i) ret[i] = ReadInt; return ret; }
            public long[] ReadLongArray(long N) { var ret = new long[N]; for (long i = 0; i < N; ++i) ret[i] = ReadLong; return ret; }
        }
    }
}