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: Runtime Error)

import java.io.IOException;
import java.io.InputStream;
import java.util.*;

public class Main {

    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
         
        int n = sc.nextInt();
        int k = sc.nextInt();
        
        jlist l = new jlist();

        for(int i=0;i<n;i++){
        	l.addLast(sc.nextInt());
        }
        
        int max = Integer.MIN_VALUE;
        
        int nega = 0;
        for(int i=k;i>0;i-=2){
        	max = Math.max(max, l.getMax(k,nega));
        	nega += 1;
        }
        

        System.out.println(max);
        
    }
    
	//lowerBound
	static int lowerBound(Integer[] a, int key){
		int idx = Arrays.binarySearch(a, key, (x,y)->x.compareTo(y)>=0?1:-1);
		
		if(idx<0){
			idx = ~idx;
		}
		
		return idx;
	}
	static int lowerBound(ArrayList<Integer> a, int key){
		int idx = Collections.binarySearch(a, key, (x,y)->x.compareTo(y)>=0?1:-1);
		
		if(idx<0){
			idx = ~idx;
		}
		
		return idx;
	}
	
	//ソートを崩さず挿入（lowerBoundが必要）
	static void sortedInsert(ArrayList<Integer> l, int key){
		int idx = lowerBound(l,key);
		l.add(idx,key);
	}
	
	//最大排出
	static int maxNe(ArrayList<Integer> l, int n){
		int sum = 0;
		int num = Math.min(n, l.size());
		for(int i=0; i<num;i++){
			sum += l.get(i);
		}
		
		return -sum;
	}
	

}

class jlist{
	ArrayList<Integer> q;
	
	public jlist(){
		q = new ArrayList<>();
	}
	
	void addFirst(int value){
		q.add(0,value);
	}
	
	void addLast(int value){
		q.add(value);
	}
	
	int checkF(int i){
		return q.get(i);
	}
	
	int checkL(int i){
		return q.get(q.size()-1-i);
	}
	
	int pollFirst(){
		return q.remove(0);
	}
	
	int pollLast(){
		return q.remove(q.size()-1);
	}
	
	int pollMax(){
		if(checkF(0)>checkL(0)){
			return pollFirst();
		}
		else{
			return pollLast();
		}
	}
	
	int getMax(int n, int nega){
		int pn = n-nega;
		
		int[] sum = new int[pn+1]; //fnum=iのとき
		
		ArrayList<Integer> nl = new ArrayList<>();
		
		for(int fnum=0;fnum<pn;fnum++){
			for(int i=0;i<fnum;i++){
				int c = checkF(i);
				sum[fnum] += c;
				
				if(c<0){
					sortedInsert(nl,c);
				}
			}
			
			for(int i=0;i<pn-fnum;i++){
				int c = checkL(i);
				sum[fnum] += c;
				
				if(c<0){
					sortedInsert(nl,c);
				}
			}
			
			for(int i=0;i<Math.min(nl.size(),nega);i++){
				sum[fnum] -= nl.get(i);
			}
		}
		
		int max = Integer.MIN_VALUE;
		for(int i=0;i<pn+1;i++){
			max = Math.max(max, sum[i]);
		}
		
		return max;
	}
	
	//lowerBound
	static int lowerBound(Integer[] a, int key){
		int idx = Arrays.binarySearch(a, key, (x,y)->x.compareTo(y)>=0?1:-1);
		
		if(idx<0){
			idx = ~idx;
		}
		
		return idx;
	}
	static int lowerBound(ArrayList<Integer> a, int key){
		int idx = Collections.binarySearch(a, key, (x,y)->x.compareTo(y)>=0?1:-1);
		
		if(idx<0){
			idx = ~idx;
		}
		
		return idx;
	}
	
	//ソートを崩さず挿入（lowerBoundが必要）
	static void sortedInsert(ArrayList<Integer> l, int key){
		int idx = lowerBound(l,key);
		l.add(idx,key);
	}
	
}

class FastScanner {
	private final InputStream in = System.in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;
	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		} else {
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}
	private int readByte() {
		if (hasNextByte())
			return buffer[ptr++];
		else
			return -1;
	}
	private static boolean isPrintableChar(int c) {
		return 33 <= c && c <= 126;
	}
	public boolean hasNext() {
		while (hasNextByte() && !isPrintableChar(buffer[ptr]))
			ptr++;
		return hasNextByte();
	}
	public String next() {
		if (!hasNext())
			throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	public long nextLong() {
		if (!hasNext())
			throw new NoSuchElementException();
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while (true) {
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			} else if (b == -1 || !isPrintableChar(b)) {
				return minus ? -n : n;
			} else {
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}
	public int nextInt() {
		long nl = nextLong();
		if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
			throw new NumberFormatException();
		return (int) nl;
	}
	public double nextDouble() {
		return Double.parseDouble(next());
	}
}