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;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.IO;
using System.Numerics;


#if DEBUG
using Microsoft.VisualStudio.TestTools.UnitTesting;
#endif

namespace competitive_programming
{
    public class Program
    {
        static void Main(string[] args)
        {
#if DEBUG
            var scanner = new IO.StreamScanner(File.Open("input.txt", FileMode.Open));
#else
            var scanner = new IO.StreamScanner(Console.OpenStandardInput());
#endif

            var n = scanner.Integer();
            var k = scanner.Integer();
            var x = scanner.ScanLine().Split().Select(v => int.Parse(v)).ToList();

            IO.Printer.Out.WriteLine(GetAns(k, x));

            IO.Printer.Out.Flush();
        }

        static long GetAns(int k, List<int> x)
        {
            var ret = long.MaxValue;

            for (int i = 0; i <= x.Count() - k; i++)
            {
                ret = Math.Min(ret, GetAns(x.Skip(i).Take(k).ToList()));
            }

            return ret;
        }

        static long GetAns(List<int> x)
        {
            if (x.All(v => v <= 0) || x.All(v => v >= 0))
            {
                return Math.Max(Math.Abs(x.Min()), Math.Abs(x.Max()));
            }

            if (Math.Abs(x[0]) <= Math.Abs(x.Last()))
            {
                return Math.Abs(x[0]) * 2 + Math.Abs(x.Last());
            }
            else
            {
                return Math.Abs(x[0]) + Math.Abs(x.Last()) * 2;
            }
        }
    }

#if DEBUG
#endif

    #region INOUT

    namespace IO
    {
        using System.IO;
        using System.Text;
        using System.Globalization;

        public class Printer : StreamWriter
        {
            static Printer()
            {
                Out = new Printer(Console.OpenStandardOutput()) { AutoFlush = false };
            }

            public static Printer Out { get; set; }

            public override IFormatProvider FormatProvider
            {
                get { return CultureInfo.InvariantCulture; }
            }

            public Printer(Stream stream)
                : base(stream, new UTF8Encoding(false, true))
            {
            }

            public Printer(Stream stream, Encoding encoding)
                : base(stream, encoding)
            {
            }

            public void Write<T>(string format, T[] source)
            {
                base.Write(format, source.OfType<object>().ToArray());
            }

            public void WriteLine<T>(string format, T[] source)
            {
                base.WriteLine(format, source.OfType<object>().ToArray());
            }
        }

        public class StreamScanner
        {
            public StreamScanner(Stream stream)
            {
                str = stream;
            }

            public readonly Stream str;
            private readonly byte[] buf = new byte[1024];
            private int len, ptr;
            public bool isEof;

            public bool IsEndOfStream
            {
                get { return isEof; }
            }

            private byte read()
            {
                if (isEof) return 0;
                if (ptr < len) return buf[ptr++];
                ptr = 0;
                if ((len = str.Read(buf, 0, 1024)) > 0) return buf[ptr++];
                isEof = true;
                return 0;
            }

            public char Char()
            {
                byte b;
                do b = read(); while ((b < 33 || 126 < b) && !isEof);
                return (char)b;
            }

            public string Scan()
            {
                var sb = new StringBuilder();
                for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
                    sb.Append(b);
                return sb.ToString();
            }

            public string ScanLine()
            {
                var sb = new StringBuilder();
                for (var b = Char(); b != '\n'; b = (char)read())
                    if (b == 0) break;
                    else if (b != '\r') sb.Append(b);
                return sb.ToString();
            }

            public long Long()
            {
                if (isEof) return long.MinValue;
                long ret = 0;
                byte b;
                var ng = false;
                do b = read(); while (b != 0 && b != '-' && (b < '0' || '9' < b));
                if (b == 0) return long.MinValue;
                if (b == '-')
                {
                    ng = true;
                    b = read();
                }
                for (; ; b = read())
                {
                    if (b < '0' || '9' < b)
                        return ng ? -ret : ret;
                    ret = ret * 10 + b - '0';
                }
            }

            public int Integer()
            {
                return (isEof) ? int.MinValue : (int)Long();
            }

            public double Double()
            {
                var s = Scan();
                return s != "" ? double.Parse(s, CultureInfo.InvariantCulture) : double.NaN;
            }

            static T[] enumerate<T>(int n, Func<T> f)
            {
                var a = new T[n];
                for (int i = 0; i < n; ++i) a[i] = f();
                return a;
            }

            public char[] Char(int n)
            {
                return enumerate(n, Char);
            }

            public string[] Scan(int n)
            {
                return enumerate(n, Scan);
            }

            public double[] Double(int n)
            {
                return enumerate(n, Double);
            }

            public int[] Integer(int n)
            {
                return enumerate(n, Integer);
            }

            public long[] Long(int n)
            {
                return enumerate(n, Long);
            }
        }
    }

    #endregion
}