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++14 (Clang 3.8.0) (judge verdict: Accepted)

/*
　　　  ∧＿∧　やあ
　　 （´・ω・｀)　　　　　/　　　　　ようこそ、バーボンハウスへ。
　　 ／∇y:::::＼　　　 [￣]　　　　　このテキーラはサービスだから、まず飲んで落ち着いて欲しい。
　　 |:⊃:|:::::|　　　|──|
￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣|　うん、「また」なんだ。済まない。
￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣|￣　  仏の顔もって言うしね、謝って許してもらおうとも思っていない。
￣￣￣￣￣￣￣￣￣￣￣￣￣￣／|
　　　　∇　∇　∇　∇　　　／.／|　　　でも、この提出を見たとき、君は、きっと言葉では言い表せない
　　　　┴　┴　┴　┴　／ ／　  |　　　「ときめき」みたいなものを感じてくれたと思う。
￣￣￣￣￣￣￣￣￣￣|／　　  |　　　殺伐としたコンテストの中で、そういう気持ちを忘れないで欲しい
￣￣￣￣￣￣￣￣￣￣　　　　 |　　　そう思って、この提出を投げたんだ。
　　　(⊆⊇)　(⊆⊇)　(⊆⊇)　　|
　    ||　　 ||　　||　　|　　　 じゃあ、判定を聞こうか。
　　.／|＼　／|＼ ／|＼
*/

#include <iostream>
#include <cstdlib>
#include <algorithm>
#include <array>
#include <bitset>
#include <climits>
#include <cmath>
#include <cstdio>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <string>
#include <vector>
using namespace std;
#define fst first
#define snd second
#define mp make_pair
#define ALL(obj) (obj).begin(),(obj).end()
#define FOR(i,a,b) for(int i=(a);i<(b);i++)
#define RFOR(i,a,b) for(int i = (b-1);i>=a;i--)
#define REP(i,n)  FOR(i,0,n)
#define RREP(i,n) RFOR(i,0,n) 
#define SIZE(x) ((int)(x).size())
#define debug(x) cerr << #x << " -> " << x << " (line:" << __LINE__ << ")" << '\n';
#define debugpair(x, y) cerr << "(" << #x << ", " << #y << ") -> (" << x << ", " << y << ") (line:" << __LINE__ << ")" << '\n';
typedef long long lint;
typedef pair<int, int> pint;
typedef pair<lint, lint> plint;
typedef vector<lint> vec;
typedef vector<vector<lint>> matrix;
typedef priority_queue<lint> p_que;
typedef priority_queue<lint, vector<lint>, greater<lint>> p_que_rev;
const lint INF = INT_MAX;
const lint LINF = LLONG_MAX;
const lint MOD = 1000000000 + 7;
const double EPS = 1e-9;
const double PI = acos(-1);
const int di[]{0, -1, 0, 1, -1, -1, 1, 1};
const int dj[]{1, 0, -1, 0, 1, -1, -1, 1};

lint gcd(lint a, lint b) {
    lint r;
    while (b != 0) {
        r = a % b;
        a = b; 
        b = r;
    }
    return a;
}

lint lcm(lint a, lint b) {
    return (a / gcd(a, b)) * b;
}

lint power(lint x, lint n, lint mod = MOD) {
    lint ret = 1;
    while(n > 0) {
        if(n & 1){
            (ret *= x) %= mod;
        }
        (x *= x) %= mod;
        n >>= 1;
    }
    return ret;
}

vector<lint> make_power(int n, lint base){
    lint num = 1;
    vector<lint> ret;
    for (int i=0; i<=n; ++i){
        ret.push_back(num);
        num *= base;
    }
    return ret;
}

int main()
{
    cin.tie(0);
    ios_base::sync_with_stdio(false);
    lint n, k;
    cin >> n >> k;
    vector<lint> v(n);
    REP(i, n){
        cin >> v[i];
    }
    lint ans = -LINF;
    lint value = 0;
    lint rest;
    p_que_rev queue;
    vector<bool> isUsed(n, false);
    REP(i, k+1){
        REP(j, k-i+1){
            queue = p_que_rev();
            REP(l, n){
                isUsed[l] = false;
            }
            value = 0;
            rest = k - i - j;
            REP(l, i){
                if(!(l < n)){
                    continue;
                }
                if(!isUsed[l]){
                    value += v[l];
                    queue.push(v[l]);
                    isUsed[l] = true;
                }
            }
            REP(l, j){
                if(!(n-1-l >= 0)){
                    continue;
                }
                if(!isUsed[n-1-l]){
                    value += v[n-1-l];
                    queue.push(v[n-1-l]);
                    isUsed[n-1-l] = true;
                }
            }
            while(rest > 0 && !queue.empty()){
                auto t = queue.top();
                queue.pop();
                if(t < 0){
                    value -= t;
                }
                rest--;
            }
            //cout << "(" << i << ", " << j << ") : rest : " << rest << " -> " << value << endl;
            ans = max(ans, value);
        }
    }
    cout << ans << endl;
    return 0;
}