Problem:
Score : 700 points

Problem Statement

There are N panels arranged in a row in Takahashi's house, numbered 1 through N. The i-th panel has a number A_i written on it. Takahashi is playing by throwing balls at these panels.

Takahashi threw a ball K times. Let the panel hit by a boll in the i-th throw be panel p_i. He set the score for the i-th throw as i \times A_{p_i}.

He was about to calculate the total score for his throws, when he realized that he forgot the panels hit by balls, p_1,p_2,...,p_K. The only fact he remembers is that for every i (1 ≦ i ≦ K-1), 1 ≦ p_{i+1}-p_i ≦ M holds. Based on this fact, find the maximum possible total score for his throws.

Constraints

1 ≦ M ≦ N ≦ 100,000

1 ≦ K ≦ min(300,N)

1 ≦ A_i ≦ 10^{9}

Partial Scores

In the test set worth 100 points, M = N.

In the test set worth another 200 points, N ≦ 300 and K ≦ 30.

In the test set worth another 300 points, K ≦ 30.

Input

The input is given from Standard Input in the following format:

N M K
A_1 A_2 … A_N

Output

Print the maximum possible total score for Takahashi's throws.

Sample Input 1

5 2 3
10 2 8 10 2

Sample Output 1

56

The total score is maximized when panels 1,3 and 4 are hit, in this order.

Sample Input 2

5 5 2
5 2 10 5 9

Sample Output 2

28

This case satisfies the additional constraint M = N for a partial score.

Sample Input 3

10 3 5
3 7 2 6 9 4 8 5 1 1000000000

Sample Output 3

5000000078

Solution in Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

{-# LANGUAGE ScopedTypeVariables #-}
import Control.Applicative
import Control.Monad
import Control.Monad.State
import Control.DeepSeq
import Data.Array
import Data.Bits
import Data.Char
import Data.Functor.Identity
import Data.List
import Data.Maybe
import Data.Ord
import Data.Tree
import Data.Tuple
import qualified System.IO
import qualified Data.Map as M
import qualified Data.Set as S
import qualified Data.Sequence as Q
import qualified Data.ByteString.Char8 as B

main = do
  [n,m,k] <- getInts
  as <- listArray (1,n) <$> getInts
  let
    dp =
     if n == m
     then 
      array ((0,0),(n,k)) $
      [((n',0),0) | n' <- [0..n]] ++
      [((0,k'),0) | k' <- [1..k]] ++
      [((n',k'), k' * as!n' + dpMax!(n'-1,k'-1)) | n' <- [1..n], k' <- [1..k], let n0 = max (k'-1) (n'-m)]
     else
      array ((0,0),(n,k)) $
      [((n',0),0) | n' <- [0..n]] ++
      [((0,k'),0) | k' <- [1..k]] ++
      [((n',k'), maximum [k' * as!n' + dp!(n'',k'-1) | n'' <- [n0..n'-1]]) | n' <- [1..n], k' <- [1..k], let n0 = max (k'-1) (n'-m)]
    dpMax = array ((0,0),(n,k)) $
      [((k',k'),dp!(k',k')) | k' <- [0..k]] ++
      [((n',k'),maximum [dp!(n',k'), dpMax!(n'-1,k')]) | k' <- [0..k], n' <- [k'+1..n]]
    ans = maximum [dp!(n',k) | n' <- [k..n]]
  print ans
  -- print dp


type Z = Int
type Q = Rational
type R = Double
type S = String

fint :: (Integral a, Num b) => a -> b
fint = fromIntegral

getInt = fst . fromJust . B.readInt <$> B.getLine
getIntPair = (\[a,b]->(a,b)) <$> getInts
getInts = map (fst . fromJust . B.readInt) . B.words <$> B.getLine
getStr = B.unpack <$> B.getLine

yesNo :: Bool -> String
yesNo True = "Yes"
yesNo False = "No"

printList :: (Show a) => [a] -> IO ()
printList = putStrLn . unwords . map show

readLnList :: (Read a) => IO [a]
readLnList = map read . words <$> getLine


-----  Union-find
type UnionFindT v m a = StateT (M.Map v (UnionFindVal v)) m a
newtype UnionFindVal v = UnionFindVal v

runUnionFindT :: (Monad m) => UnionFindT v m a -> m a
runUnionFindT = flip evalStateT $ M.empty

runUnionFind = runIdentity . runUnionFindT

ufFresh :: (Monad m, Ord v) => v -> UnionFindT v m ()
ufFresh v = modify $ M.insert v (UnionFindVal v)

ufClass :: (Monad m, Ord v) => v -> UnionFindT v m v
ufClass v = do
  (UnionFindVal pv) <- gets (M.! v)
  if v == pv
    then return v
    else do
      c <- ufClass pv
      modify $ M.insert v (UnionFindVal c)
      return c

ufUnify v w = do
  cv <- ufClass v
  cw <- ufClass w
  modify $ M.insert cw (UnionFindVal cv)
  return $ cv /= cw