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.Linq;
using System.Text;
using System.Threading.Tasks;
using static System.Console;

class Program
{
    static void Main(string[] args)
    {
        new Program().Calc();
    }

    Scanner cin;

    public Program() { }

    bool chmax<T>(ref T a, T b) where T : IComparable<T> { if (a.CompareTo(b) < 0) { a = b; return true; } return false; }
    bool chmin<T>(ref T a, T b) where T : IComparable<T> { if (b.CompareTo(a) < 0) { a = b; return true; } return false; }

    void Calc()
    {
        cin = new Scanner();

        int N = cin.nextInt();
        int K = cin.nextInt();

        int[] V = cin.ArrayInt(N);

        // 操作のすべての組み合わせ
        // 4通りの操作があるので2ビット使っている

        int sousaCount = (1 << K * 2);

        int maxValue = 0;

        for (int i = 0; i < sousaCount; ++i)
        {
            List<int> list = new List<int>();
            list.AddRange(V);

            // 手に持ってる宝石
            PriorityQueue<int> queue = new PriorityQueue<int>(N, Compare);

            int totalValue = 0;

            for (int j = 0; j < K; ++j)
            {
                int sousa = ((i >> j * 2) & 3);

                switch (sousa)
                {
                    case 0:
                        if (list.Count != 0)
                        {
                            int jewelValue = list.ElementAt(0);
                            totalValue += jewelValue;
                            queue.Enqueue(jewelValue);
                            list.RemoveAt(0);
                        }
                        break;
                    case 1:
                        if (list.Count != 0)
                        {
                            int jewelValue = list.ElementAt(list.Count - 1);
                            totalValue += jewelValue;
                            queue.Enqueue(jewelValue);
                            list.RemoveAt(list.Count - 1);
                        }
                        break;
                    case 2:
                        if (queue.Count() >= 1)
                        {
                            int jewelValue = queue.Dequeue();
                            totalValue -= jewelValue;
                            list.Insert(0, jewelValue);
                        }
                        break;
                    case 3:
                        if (queue.Count() >= 1)
                        {
                            int jewelValue = queue.Dequeue();
                            totalValue -= jewelValue;
                            list.Add(jewelValue);
                        }
                        break;
                }

                if (maxValue < totalValue) { maxValue = totalValue; }
            }
        }

        WriteLine(maxValue);
    }

    int Compare(int a, int b)
    {
        if (a < b) { return -1; }
        else if (a > b) { return 1; }
        else { return 0; }
    }
}

class PriorityQueue<T>
{
    private readonly List<T> m_list;
    private readonly Func<T, T, int> m_compare;
    private int m_count;
    public PriorityQueue(int capacity, Func<T, T, int> compare)
    {
        m_list = new List<T>(capacity);
        m_compare = compare;
        m_count = 0;
    }
    private int Add(T value)
    {
        if (m_count == m_list.Count)
        {
            m_list.Add(value);
        }
        else
        {
            m_list[m_count] = value;
        }
        return m_count++;
    }
    private void Swap(int a, int b)
    {
        T tmp = m_list[a];
        m_list[a] = m_list[b];
        m_list[b] = tmp;
    }
    public int Count()
    {
        return m_count;
    }
    public void Enqueue(T value)
    {
        int c = Add(value);
        while (c > 0)
        {
            int p = (c - 1) / 2;
            if (m_compare(m_list[c], m_list[p]) < 0) { Swap(p, c); } else { break; }
            c = p;
        }
    }
    public T Dequeue()
    {
        T value = m_list[0];
        m_list[0] = m_list[--m_count];
        int p = 0;
        while (true)
        {
            int c1 = p * 2 + 1;
            int c2 = p * 2 + 2;
            if (c1 >= m_count) { break; }
            int c = (c2 >= m_count || m_compare(m_list[c1], m_list[c2]) < 0) ? c1 : c2;
            if (m_compare(m_list[c], m_list[p]) < 0) { Swap(p, c); } else { break; }
            p = c;
        }
        return value;
    }
}

public static class StringExtension
{
    public static char GetChar1(this string str, int indexOneBase)
    {
        return str[indexOneBase - 1];
    }
}

class Scanner
{
    string[] s;
    int i;

    char[] cs = new char[] { ' ' };

    public Scanner()
    {
        s = new string[0];
        i = 0;
    }

    public string next()
    {
        if (i < s.Length) return s[i++];
        string st = Console.ReadLine();
        while (st == "") st = Console.ReadLine();
        s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        if (s.Length == 0) return next();
        i = 0;
        return s[i++];
    }

    public int nextInt()
    {
        return int.Parse(next());
    }
    public int[] ArrayInt(int N, int add = 0)
    {
        int[] Array = new int[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextInt() + add;
        }
        return Array;
    }

    public long nextLong()
    {
        return long.Parse(next());
    }

    public long[] ArrayLong(int N, long add = 0)
    {
        long[] Array = new long[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextLong() + add;
        }
        return Array;
    }

    public double nextDouble()
    {
        return double.Parse(next());
    }


    public double[] ArrayDouble(int N, double add = 0)
    {
        double[] Array = new double[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextDouble() + add;
        }
        return Array;
    }
}