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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
using ll=long long;
//-10 8 2 1 2 6
//4だとして？
//40,31,22,13,04で取れる。
//3個とって１個戻せる
// (4-1)/2=1まで戻す可能性ある。5個とるなら２個戻すとか。
//そんなことないか。4/2=2個もどすか　5/2=2か
//50個の１００通りなら全探索できそう
//全部の累積和とって、6 4 なら２個ずつ引く。
//３個とって戻すなら？累積和から３とって、一番低い要素を1個抜く
//-10 8 2 1 2 6 -20 8 3 4 2 1
//12 8とか
//8とるか、7とって１戻すか、6とって２戻すか、5とって３戻すか、４とって４戻すか。
//50,100だと
//100とる?、50とって50=0戻す、49とって51=1戻す..
//50C1+50C2+...50!くらいありえる。大きすぎるかも
//違うか。とりかたはせいぜい50通り+50とか。
//とったら、つどsortしてlower?
//負だけ取り除く感じ。
//最小は、Kは偶数だったら0、奇数だったら1
//全探索でまにあっちゃうかな
//再帰で全通り可能？めもりたらなそう
//左からなんこ、右からなんことって、なんこもどす、みたいな。
//戻す数？50100だったら、25個もどすとかか50個もどす、までか。
//50 30なら？30/2=15個まで
//sortしておしりからとってくるかんじ？本当に原始的すぎて･･･
//5,6 4個しかとれないN-K)%2が重要か
//5,8なら5,6とおなじ 5,10も5,12も。
//-1 -2 -3 -4 5 -6 -7 -8 -9 -10
//問題読み違えていた。K回まで操作を行うことが出来ます･･･。
int main(){
  ll N,K;
  cin>>N>>K;
  vector<ll> base(N,0);
  for(int i=0; i<N; i++){
    ll V; cin>>V; base[i]=V;
  }
  ll k=min(N,K), ans=0, check=0;  
  ll back=k/2;
  K=min(K,N+N/2);
  if((N-K)%2!=0 || K-N>0) check++;
  k+=check;
  for(int i=0; i<=back; i++){//戻す数
    ll take=min(N,K-i);
    for(int lft=0; lft<=take; lft++){//左からとる個数
      ll tmp=0;
      vector<ll> W(0,0);
      for(int j=0; j<lft; j++){
        W.emplace_back(base[j]);
        tmp+=base[j];
      }
      for(int j=0; j<take-lft; j++){
        W.emplace_back(base[N-1-j]);
        tmp+=base[N-1-j];
      }
      sort(W.begin(), W.end());
      for(int j=0; j<i; j++)
        tmp-=W[j];
      ans=max(ans,tmp);
    }
  }
  cout<<ans<<endl;
}