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: Accepted)

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

partial class Solver
{
    public void Run()
    {
        var N = ni();
        var K = ni();
        var V = ni(N);
        long ans = 0;

        for (int left = 0; left <= K; left++)
        {
            for (int right = 0; left + right <= K && left + right <= N; right++)
            {
                var canDel = K - (left + right);

                var inner = new List<int>();
                inner.AddRange(V.Take(left));
                inner.AddRange(V.Reverse().Take(right));

                inner.Sort((v1, v2) => -v1.CompareTo(v2));

                while (canDel > 0 && inner.Count > 0 && inner.Last() < 0)
                {
                    canDel--;
                    inner.RemoveAt(inner.Count - 1);
                }

                ans = Math.Max(ans, inner.Sum());
            }
        }

        cout.WriteLine(ans);
    }
}


// PREWRITEN CODE BEGINS FROM HERE
partial class Solver : Scanner
{
    public static void Main(string[] args)
    {
        new Solver(Console.In, Console.Out).Run();
    }

    TextReader cin;
    TextWriter cout;

    public Solver(TextReader reader, TextWriter writer)
        : base(reader)
    {
        this.cin = reader;
        this.cout = writer;
    }
    public Solver(string input, TextWriter writer)
        : this(new StringReader(input), writer)
    {
    }

    public int ni() { return NextInt(); }
    public int[] ni(int n) { return NextIntArray(n); }
    public long nl() { return NextLong(); }
    public long[] nl(int n) { return NextLongArray(n); }
    public double nd() { return NextDouble(); }
    public string ns() { return Next(); }
}

public class Scanner
{
    private TextReader Reader;
    private Queue<String> TokenQueue = new Queue<string>();
    private readonly CultureInfo ci = CultureInfo.InvariantCulture;

    public Scanner()
        : this(Console.In)
    {
    }

    public Scanner(TextReader reader)
    {
        this.Reader = reader;
    }

    public int NextInt() { return Int32.Parse(Next(), ci); }
    public long NextLong() { return Int64.Parse(Next(), ci); }
    public double NextDouble() { return double.Parse(Next(), ci); }
    public string[] NextArray(int size)
    {
        var array = new string[size];
        for (int i = 0; i < size; i++) array[i] = Next();
        return array;
    }
    public int[] NextIntArray(int size)
    {
        var array = new int[size];
        for (int i = 0; i < size; i++) array[i] = NextInt();
        return array;
    }

    public long[] NextLongArray(int size)
    {
        var array = new long[size];
        for (int i = 0; i < size; i++) array[i] = NextLong();
        return array;
    }

    public String Next()
    {
        if (TokenQueue.Count == 0)
        {
            if (!StockTokens()) throw new InvalidOperationException();
        }
        return TokenQueue.Dequeue();
    }

    public bool HasNext()
    {
        if (TokenQueue.Count > 0)
            return true;
        return StockTokens();
    }

    private bool StockTokens()
    {
        while (true)
        {
            var line = Reader.ReadLine();
            if (line == null) return false;
            var tokens = line.Trim().Split(" ".ToCharArray(), StringSplitOptions.RemoveEmptyEntries);
            if (tokens.Length == 0) continue;
            foreach (var token in tokens)
                TokenQueue.Enqueue(token);
            return true;
        }
    }
}