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.Net;
using System.Text;


namespace AtC
{
    class Program
    {
        static void Main(string[] args)
        {
            var nk = ReadIntArray();
            int N = nk[0], K = nk[1];
            var V = ReadIntArray();
            var concat = V.Concat(V).Select(val => (long) val).ToArray();

            long max = long.MinValue;
            for (int n = 0; n < Math.Min(N, K); n++) //n個合計で取ることを考える
            {
                int f = K - n; //f回まで戻す操作をしていい

                for (int l = 0; l <= n; l++) //左からl個とるとき
                {
                    var array = concat.Skip(N - l)
                                      .Take(n)
                                      .ToArray();
                    var sum = array.Sum();
                    var negateSum = concat.Skip(N - l)
                                          .Take(n)
                                          .Where(val => val < 0)
                                          .OrderBy(val => val)
                                          .Take(f)
                                          .Sum();
                    max = Math.Max(max, sum - negateSum);
                }
            }

            Out(max);
        }

        //最小公倍数
        static int LCM(int num1, int num2)
        {
            var gcd = GCD(num1, num2);
            return num1 * (num2 / gcd);
        }

        static long LCM(long num1, long num2)
        {
            var gcd = GCD(num1, num2);
            return num1 * (num2 / gcd);
        }

        //最大公約数
        static int GCD(int num1, int num2)
        {
            int a = Math.Max(num1, num2);
            int b = Math.Min(num1, num2);
            int mod;
            while ((mod = a % b) != 0)
            {
                a = b;
                b = mod;
            }

            return b;
        }

        static long GCD(long num1, long num2)
        {
            long a = Math.Max(num1, num2);
            long b = Math.Min(num1, num2);
            long mod;
            while ((mod = a % b) != 0)
            {
                a = b;
                b = mod;
            }

            return b;
        }

        static int[] ReadIntArray()
        {
            return Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        }

        static int ReadInt()
        {
            return int.Parse(Console.ReadLine());
        }

        static long[] ReadLongArray()
        {
            return Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
        }

        static long ReadLong()
        {
            return long.Parse(Console.ReadLine());
        }

        static string ReadString()
        {
            return Console.ReadLine();
        }

        static void Out(object o)
        {
            Console.WriteLine(o);
        }
    }

    static class EnumerableExtension
    {
        public delegate void Function<in T>(T val);

        public static void ForEach<T>(this IEnumerable<T> enumerable, Function<T> function)
        {
            foreach (var x in enumerable)
            {
                function(x);
            }
        }
    }

//    class PriorityQueue<T>
//    {
//        private readonly List<Tuple<int, T>> _list = new List<Tuple<int, T>>();
//
//        public PriorityQueue()
//        {
//        }
//
//        public void Push(T item, int priority)
//        {
//            var itemIndex = _list.Count;
//            _list.Add(Tuple.Create(priority, item));
//        }
//
//        public T Pop()
//        {
//        }
//
//        public T Peek()
//        {
//            return _list[0].Item2;
//        }
//
//        private void Swap(int index1, int index2)
//        {
//            var tmp = _list[index1];
//            _list[index1] = _list[index2];
//            _list[index2] = tmp;
//        }
//    }

    class UnionFind
    {
        private readonly int[] _array;

        public UnionFind(int N)
        {
            _array = new int[N];
            for (int i = 0; i < N; i++)
            {
                _array[i] = i;
            }
        }

        public int GetRootNode(int n)
        {
            if (_array[n] == n) return n;
            return _array[n] = GetRootNode(_array[n]);
        }

        public void UnionGroup(int a, int b)
        {
            var rootA = GetRootNode(a);
            var rootB = GetRootNode(b);
            if (rootA == rootB) return;
            _array[rootA] = rootB;
        }

        public bool IsSameGroup(int a, int b) => GetRootNode(a) == GetRootNode(b);

        public bool IsRoot(int n) => _array[n] == n;
    }
}