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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.math.*;
import java.security.KeyStore.Entry;
import java.util.*;

public class Main {
	private static boolean[] vis;
	private static long[] dist;
	public static void merge(int arr[], int l, int m, int r) 
    { 
        // Find sizes of two subarrays to be merged 
        int n1 = m - l + 1; 
        int n2 = r - m; 
  
        /* Create temp arrays */
        int L[] = new int [n1]; 
        int R[] = new int [n2]; 
  
        /*Copy data to temp arrays*/
        for (int i=0; i<n1; ++i) 
            L[i] = arr[l + i]; 
        for (int j=0; j<n2; ++j) 
            R[j] = arr[m + 1+ j]; 
  
  
        /* Merge the temp arrays */
  
        // Initial indexes of first and second subarrays 
        int i = 0, j = 0; 
  
        // Initial index of merged subarry array 
        int k = l; 
        while (i < n1 && j < n2) 
        { 
            if (L[i] <= R[j]) 
            { 
                arr[k] = L[i]; 
                i++; 
            } 
            else
            { 
                arr[k] = R[j]; 
                j++; 
            } 
            k++; 
        } 
  
        /* Copy remaining elements of L[] if any */
        while (i < n1) 
        { 
            arr[k] = L[i]; 
            i++; 
            k++; 
        } 
  
        /* Copy remaining elements of R[] if any */
        while (j < n2) 
        { 
            arr[k] = R[j]; 
            j++; 
            k++; 
        } 
    } 
	 public static void sort(int arr[], int l, int r) 
	    { 
	        if (l < r) 
	        { 
	            // Find the middle point 
	            int m = (l+r)/2; 
	  
	            // Sort first and second halves 
	            sort(arr, l, m); 
	            sort(arr , m+1, r); 
	  
	            // Merge the sorted halves 
	            merge(arr, l, m, r); 
	        } 
	    } 
	 private static int gcd(int n, int l) {
	        if (l == 0)
	            return n;
	        return gcd(l, n % l);
	    }
	 public static void dfs(ArrayList<Pair>[] gr,int v)
	    {
	         vis[v]=true;
	         ArrayList<Pair> arr=gr[v];
	         for(int i=0;i<arr.size();i++)
	         {
	             if(!vis[arr.get(i).v])
	             {  
	            	 dfs(gr,arr.get(i).v);
	             }
	         }
	    }
	 private static class Pairs implements Comparable<Pairs>{
	        String v;int i;int j;
	        public Pairs(String a,int b,int c){
	            v=a;
	            i=b;
	            j=c;
	        }
	        @Override
	        public int compareTo(Pairs arg0) {
	            {
	            	if(!this.v.equals(arg0.v))
	            		return this.v.compareTo(arg0.v);
	            	else
	            		return arg0.i-this.i;
	            }
	        }
	    }
	 private static class Pair implements Comparable<Pair>{
	        int v,i;Pair j;
	        public Pair(int a,int b){
	            v=a;
	            i=b;
	        }
	        public Pair(int a,Pair b)
	        {
	            v=a;
	            j=b;
	        }
	        @Override
	        public int compareTo(Pair arg0) {
	            {
	            	return this.v-arg0.v;
	            }
	        }
	    }
	public static void main(String[] args) throws Exception
	{
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int k=sc.nextInt();
		long[] arr=new long[n];
		for(int i=0;i<n;i++)	arr[i]=sc.nextLong();
		long max=0;
		for(int l=0;l<n;l++)
		{
			for(int r=0;r<n;r++)
			{
				int op=k;
				if((l+r)<=op && (l+r)<n)
				{
					op-=(l+r);
					ArrayList<Long> arr2=new ArrayList<>();
					for(int i=0;i<l;i++)
						arr2.add(arr[i]);
					for(int i=n-1;i>=n-r;i--)
						arr2.add(arr[i]);
					arr2.sort(null);
					for(int i=0;i<arr2.size();i++)
					{
						if(arr2.get(i)<0 && op>0)
						{
							arr2.set(i,(long) 0);op--;
						}
					}
					long sum=0;
					for(int i=0;i<arr2.size();i++)
						sum+=arr2.get(i);
					if(sum>max)	max=sum;
				}
			}
		}
		System.out.println(max);
	}
}