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;

class Program
{
    static Scanner sc = new Scanner();
    static void Main(string[] args)
    {
        var N = sc.ReadInt();
        var K = sc.ReadInt();
        var V = sc.ReadIntArray(N);

        var ans = 0;

        for (int l = 0; l < K; l++)
        {
            for (int r = 0; r < K - l; r++)
            {
                if (l + r > N) continue;
                for (int d = 0; d <= K - l - r; d++)
                {
                    var list = new List<int>();
                    for (int i = 0; i < l; i++) list.Add(V[i]);
                    for (int i = 0; i < r; i++) list.Add(V[N - i - 1]);
                    ans = Math.Max(ans, list.OrderBy(x => x).Skip(d).Sum());
                }
            }
        }

        Console.WriteLine(ans);
    }
}

class Modulo
{
    public readonly int MOD;
    private readonly List<int> Facs = new List<int>() { 1 };

    public Modulo(int mod = 1000000007) { this.MOD = mod; }
    public int Mul(int a, int b) { return (int)(Math.BigMul(a, b) % MOD); }
    public int Div(int a, int b) { return Mul(a, Pow(b, MOD - 2)); }
    public int Pow(int a, int n)
    {
        switch (n)
        {
            case 0:
                return 1;
            case 1:
                return a;
            default:
                int p1 = Pow(a, n / 2);
                int p2 = Mul(p1, p1);
                return ((n % 2) == 0) ? p2 : Mul(p2, a);
        }
    }
    public int Fac(int n)
    {
        for (int i = this.Facs.Count; i <= n; i++)
        {
            this.Facs.Add(Mul(i, Facs[i - 1]));
        }
        return this.Facs[n];
    }
    public int nPr(int n, int r) => Div(Fac(n), Fac(n - r));
    public int nCr(int n, int r)
    {
        if (n < r) return 0;
        if (n == r) return 1;
        int res = Fac(n);
        res = Div(res, Fac(r));
        res = Div(res, Fac(n - r));
        return res;
    }
}

class Debug
{
    public static void Dump<T>(T[,] array)
    {
        Console.WriteLine();
        var h = array.GetLength(0);
        var w = array.GetLength(1);

        for (int r = 0; r < h; r++)
        {
            for (int c = 0; c < w; c++)
            {
                Console.Write(array[r, c]);
                Console.Write(" ");
            }
            Console.WriteLine();
        }
        Console.WriteLine();
    }
    public static void Dump<T>(T[] array)
    {
        Console.WriteLine();
        Console.WriteLine(string.Join(" ", array));
        Console.WriteLine();
    }
}

class Scanner
{
    string[] S = new string[0];
    int Index = 0;
    char[] Separators = new char[] { ' ' };

    public string Next()
    {
        if (this.Index < this.S.Length) return this.S[this.Index++];
        var line = "";
        while (line == "") line = Console.ReadLine();
        this.S = line.Split(this.Separators, StringSplitOptions.RemoveEmptyEntries);
        if (this.S.Length == 0) return this.Next();
        this.Index = 0;
        return this.S[this.Index++];
    }

    public string ReadStr()
    {
        return this.Next();
    }

    public char ReadChar()
    {
        return this.Next()[0];
    }

    public int ReadInt()
    {
        return int.Parse(this.Next());
    }

    public uint ReadUInt()
    {
        return uint.Parse(this.Next());
    }

    public long ReadLong()
    {
        return long.Parse(this.Next());
    }

    public int[] ReadIntArray(int n)
    {
        var array = new int[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadInt();
        }
        return array;
    }

    public long[] ReadLongArray(int n)
    {
        var array = new long[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadLong();
        }
        return array;
    }

    public char[] ReadCharArray(int n)
    {
        var array = new char[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadChar();
        }
        return array;
    }

    public string[] ReadStrArray(int n)
    {
        var array = new string[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadStr();
        }
        return array;
    }
}

class HashMap<K, V> : Dictionary<K, V> where V : new()
{
    private V DefaltValue = new V();
    public HashMap() { }
    public HashMap(V defaultValue)
    {
        this.DefaltValue = new V();
    }
    new public V this[K i]
    {
        get
        {
            V v;
            return TryGetValue(i, out v) ? v : base[i] = this.DefaltValue;
        }
        set { base[i] = value; }
    }
}

class PriorityQueue<T> where T : IComparable<T>
{
    public readonly T[] Array;
    public readonly bool Greater;
    public int Count { get; private set; } = 0;

    public PriorityQueue(int capacity, bool greater = true)
    {
        this.Array = new T[capacity];
        this.Greater = greater;
    }

    public void Enqueue(T item)
    {
        this.Array[this.Count] = item;
        this.Count += 1;
        this.UpHeap();
    }

    public T Dequeue()
    {
        this.Swap(0, this.Count - 1);
        this.Count -= 1;
        this.DownHeap();

        return this.Array[this.Count];
    }

    public T Peek()
    {
        return this.Array[0];
    }

    private void UpHeap()
    {
        var n = this.Count - 1;
        while (n != 0)
        {
            var parent = (n - 1) / 2;

            if (this.Array[n].CompareTo(this.Array[parent]) > 0)
            {
                this.Swap(n, parent);
                n = parent;
            }
            else
            {
                break;
            }
        }
    }

    private void DownHeap()
    {
        var parent = 0;
        while (true)
        {
            var child = 2 * parent + 1;
            if (child > this.Count - 1) break;

            if (child < this.Count - 1 && this.Compare(this.Array[child], this.Array[child + 1]) < 0)
            {
                child += 1;
            }

            if (this.Compare(this.Array[parent], this.Array[child]) < 0)
            {
                this.Swap(parent, child);
                parent = child;
            }
            else
            {
                break;
            }
        }
    }

    private int Compare(T a, T b)
    {
        var c = a.CompareTo(b);
        if (!this.Greater)
        {
            c = -c;
        }
        return c;
    }

    private void Swap(int a, int b)
    {
        var tmp = this.Array[a];
        this.Array[a] = this.Array[b];
        this.Array[b] = tmp;
    }
}