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.Linq;
using System.Diagnostics;
using System.Text;
using System.Threading.Tasks;
using System.Numerics;
using System.IO;
using static System.Math;
using static Math2;
using static io;


class Program
{
    static void Main(string[] args)
    {
        var wrong_answer = new wrong_answer();
        wrong_answer.Solve();
    }
}

public class wrong_answer
{
    const int INF = 1 << 29;
    const long INFL = 1L << 60;
    const int MOD = 1000000007;
    const int MOD2 = 998244353;


    public void Solve()
    {
        var o = intm;
        var n = o[0];
        var k = o[1];
        var v = longm;
        long ans = -INFL;
        for (int i = 0; i <= Min(n, k); ++i)
        {
            for (int j = 0; i + j <= Min(n, k); ++j)
            {
                int nk = k - i - j;
                var hand = new List<long>();
                long cur = 0;
                for (int l = 0; l < i; ++l)
                {
                    hand.Add(v[l]);
                    cur += v[l];
                }
                for (int l = 0; l < j; ++l)
                {
                    hand.Add(v[n - 1 - l]);
                    cur += v[n - 1 - l];
                }
                hand.Sort();
                for (int l = 0; l < Min(nk, hand.Count()); ++l)
                {
                    if (hand[l] < 0) cur -= hand[l];
                }
                chmax(ref ans, cur);
            }
        }
        write(ans);
    }



}









public static class Math2
{
    public static long pow(long i, long n, long MOD = 1000000007)
    {
        long res = 1;
        while (n > 0)
        {
            if ((n & 1) != 0) res = res * i % MOD;
            i = i * i % MOD;
            n >>= 1;
        }
        return res;
    }
    public static int pow(int i, int n, int MOD = 1000000007)
    {
        int res = 1;
        while (n > 0)
        {
            if ((n & 1) != 0) res = res * i % MOD;
            i = i * i % MOD;
            n >>= 1;
        }
        return res;
    }

    public static long gcd(long i, long y)
    {
        while (y != 0)
        {
            var r = i % y;
            i = y;
            y = r;
        }
        return i;
    }

    public static long lcm(long i, long y)
    {
        return i * y / gcd(i, y);
    }

    public static BigInteger bgcd(BigInteger i, BigInteger y)
    {
        while (y != 0)
        {
            var r = i % y;
            i = y;
            y = r;
        }
        return i;
    }

    public static BigInteger blcm(BigInteger i, BigInteger y)
    {
        return i * y / bgcd(i, y);
    }

    public static Dictionary<long, int> primefactorization(long N)
    {

        var ret = new Dictionary<long, int>();

        for (long i = 2; i * i <= N; ++i)
        {
            int cnt = 0;
            while (N % i == 0)
            {
                cnt++;
                N /= i;
            }
            if (cnt != 0) ret[i] = cnt;

        }
        if (N >= 2) ret[N] = 1;

        return ret;

    }

    public static List<long> divisorenumrate(long N)
    {
        var ret = new List<long>();

        for (long i = 1; i * i <= N; ++i)
        {

            if (N % i == 0)
            {
                ret.Add(i);
                ret.Add(N / i);
            }

        }

        return ret;

    }

    public static void swap<T>(ref T a, ref T b)
    {
        var i = a;
        a = b;
        b = i;
    }
    public static void chmin<T>(ref T a, T b) where T : IComparable
    {
        if (a.CompareTo(b) > 0) a = b;
    }
    public static void chmax<T>(ref T a, T b) where T : IComparable
    {
        if (a.CompareTo(b) < 0) a = b;
    }

}

public static class io
{
    //in
    public static string str => Console.ReadLine();

    public static string[] strm => str.Split(' ');

    public static long[] longm => strm.Select(long.Parse).ToArray();
    public static int[] intm => strm.Select(int.Parse).ToArray();
    public static char[] charm => str.ToArray();
    public static double[] doublem => strm.Select(double.Parse).ToArray();
    public static long long1 => longm[0];
    public static int int1 => intm[0];
    public static char char1 => charm[0];
    public static double double1 => doublem[0];
    public static void write(string a) => Console.WriteLine(a);
    public static void write(params object[] i) => write(string.Join(" ", i));
    public static void write<T>(IEnumerable<T> a) => write(string.Join(" ", a));
    public static void yn(bool i) { if (i) write("Yes"); else write("No"); }

}