Problem:
Score : 400 points

Problem Statement

Your friend gave you a dequeue D as a birthday present.

D is a horizontal cylinder that contains a row of N jewels.

The values of the jewels are V_1, V_2, ..., V_N from left to right. There may be jewels with negative values.

In the beginning, you have no jewel in your hands.

You can perform at most K operations on D, chosen from the following, at most K times (possibly zero):

Operation A: Take out the leftmost jewel contained in D and have it in your hand. You cannot do this operation when D is empty.

Operation B: Take out the rightmost jewel contained in D and have it in your hand. You cannot do this operation when D is empty.

Operation C: Choose a jewel in your hands and insert it to the left end of D. You cannot do this operation when you have no jewel in your hand.

Operation D: Choose a jewel in your hands and insert it to the right end of D. You cannot do this operation when you have no jewel in your hand.

Find the maximum possible sum of the values of jewels in your hands after the operations.

Constraints

All values in input are integers.

1 \leq N \leq 50

1 \leq K \leq 100

-10^7 \leq V_i \leq 10^7

Input

Input is given from Standard Input in the following format:

N K
V_1 V_2 ... V_N

Output

Print the maximum possible sum of the values of jewels in your hands after the operations.

Sample Input 1

6 4
-10 8 2 1 2 6

Sample Output 1

14

After the following sequence of operations, you have two jewels of values 8 and 6 in your hands for a total of 14, which is the maximum result.

Do operation A. You take out the jewel of value -10 from the left end of D.

Do operation B. You take out the jewel of value 6 from the right end of D.

Do operation A. You take out the jewel of value 8 from the left end of D.

Do operation D. You insert the jewel of value -10 to the right end of D.

Sample Input 2

6 4
-6 -100 50 -2 -5 -3

Sample Output 2

44

Sample Input 3

6 3
-6 -100 50 -2 -5 -3

Sample Output 3

0

It is optimal to do no operation.

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

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

namespace Sandbox
{
    class Program
    {
        static void Main(string[] args)
        {
            var scanner = new Scanner();
            var n = scanner.GetNextAsInt();
            var k = scanner.GetNextAsInt();
            var v = scanner.ToIntArrayFromNextLine();

            var pointMax = 0;

            for (var l = 0; l <= k; l++)
            {
                for (var r = 0; l + r < n && l + r < k; r++)
                {
                    var dropNum = k - r - l;
                    var vr = v.Take(l);
                    var vl = v.Reverse().Take(r);
                    var sort = new List<int>();
                    sort.AddRange(vr);
                    sort.AddRange(vl);
                    sort.Sort();

                    while (dropNum > 0 && sort.Count > 0 && sort[0] < 0)
                    {
                        sort.RemoveAt(0);
                        dropNum--;
                    }

                    pointMax = Math.Max(pointMax, sort.Sum());
                }
            }
        }
    }

    #region String Scanner
    public class Scanner
    {
        private const char Separator = ' ';
        private readonly StreamReader _Stream = new StreamReader(Console.OpenStandardInput());
        private int _Pos;
        private string[] _Line = new string[0];

        #region get a element
        public string GetNext()
        {
            // ReSharper disable once InvertIf
            if (this._Pos >= this._Line.Length)
            {
                // ReSharper disable once PossibleNullReferenceException
                this._Line = this._Stream.ReadLine().Split(Separator);
                this._Pos = 0;
            }
            return this._Line[this._Pos++];
        }
        public int GetNextAsInt()
        {
            return int.Parse(this.GetNext());
        }
        public long GetNextAsLong()
        {
            return long.Parse(this.GetNext());
        }
        public double GetNextAsDouble()
        {
            return double.Parse(this.GetNext());
        }
        #endregion

        #region get array
        public string[] ToArrayFromNextLine()
        {
            if (this._Pos >= this._Line.Length)
            {
                // ReSharper disable once PossibleNullReferenceException
                this._Line = this._Stream.ReadLine().Split(Separator);
            }

            this._Pos = this._Line.Length;
            return this._Line;
        }
        public int[] ToIntArrayFromNextLine()
        {
            return ToIntArray(this.ToArrayFromNextLine());
        }
        public long[] ToLongArrayFromNextLine()
        {
            return ToLongArray(this.ToArrayFromNextLine());
        }
        public double[] ToDoubleArrayFromNextLine()
        {
            return ToDoubleArray(this.ToArrayFromNextLine());
        }
        #endregion

        #region convert array
        private static int[] ToIntArray(string[] array)
        {
            var result = new int[array.Length];
            for (var i = 0; i < array.Length; i++)
            {
                result[i] = int.Parse(array[i]);
            }
            return result;
        }
        private static long[] ToLongArray(string[] array)
        {
            var result = new long[array.Length];
            for (var i = 0; i < array.Length; i++)
            {
                result[i] = long.Parse(array[i]);
            }
            return result;
        }
        private static double[] ToDoubleArray(string[] array)
        {
            var result = new double[array.Length];
            for (var i = 0; i < array.Length; i++)
            {
                result[i] = double.Parse(array[i]);
            }
            return result;
        }
        #endregion
    }
    #endregion
}