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 OCaml (4.02.3) (judge verdict: Wrong Answer)

module S = Set.Make (struct type t = int * int let compare = compare end)

let () =
    let split s =
        let rec loop i cur flag acc =
            if i = String.length s then ( if flag then cur :: acc else acc) else (
                match flag, s.[i] with
                | true,  ' ' -> loop (i + 1) "" false (cur :: acc)
                | false, ' ' -> loop (i + 1) "" false acc
                | true,  v   -> loop (i + 1) (Printf.sprintf "%s%c" cur v) true acc
                | false, v   -> loop (i + 1) (Printf.sprintf "%s%c" cur v) true acc
            )
        in
        List.map int_of_string (List.rev (loop 0 "" false []))
    in
    let main () =
        let n, k = Scanf.sscanf (read_line ()) "%d %d" (fun n k -> n, k) in
        let v = Array.of_list (split (read_line ())) in
        let calc l r k =
            let rec loop i acc =
                if i = l then acc else loop (i + 1) (v.(i) :: acc)
            in
            let acc = loop 0 [] in
            let rec loop i acc =
                if i = r then acc else loop (i - 1) (v.(i) :: acc)
            in
            let acc = loop (n - 1) acc in
            let l = List.sort compare acc in
            let rec drop i list =
                if i = 0 then list else
                    match list with
                    | [] -> []
                    | hd :: tl -> if hd < 0 then drop (i - 1) tl else tl
            in
            List.fold_left (+) 0 (drop k l)
        in
        let rec loop k mx sets =
            if k = 0 then mx else
                let mx, next =
                    S.fold (fun (l, r) (mx, next) ->
                        let mx = max mx (calc l r k) in
                        let next = if l <= r then S.add (l+1, r) next else next in
                        let next = if l <  r then S.add (l, r-1) next else next in
                        mx, next) sets (mx, S.empty)
                in
                loop (k - 1) mx next
        in
        let init = S.add (0, n - 1) S.empty in
        let ans = loop k 0 init in
        Printf.printf "%d\n" ans
    in
    main ()