Problem:
Score : 500 points

Problem Statement

You are going to eat X red apples and Y green apples.

You have A red apples of deliciousness p_1,p_2, \dots, p_A, B green apples of deliciousness q_1,q_2, \dots, q_B, and C colorless apples of deliciousness r_1,r_2, \dots, r_C.

Before eating a colorless apple, you can paint it red or green, and it will count as a red or green apple, respectively.

From the apples above, you will choose the apples to eat while making the sum of the deliciousness of the eaten apples as large as possible.

Find the maximum possible sum of the deliciousness of the eaten apples that can be achieved when optimally coloring zero or more colorless apples.

Constraints

1 \leq X \leq A \leq 10^5

1 \leq Y \leq B \leq 10^5

1 \leq C \leq 10^5

1 \leq p_i \leq 10^9

1 \leq q_i \leq 10^9

1 \leq r_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X Y A B C
p_1 p_2 ... p_A
q_1 q_2 ... q_B
r_1 r_2 ... r_C

Output

Print the maximum possible sum of the deliciousness of the eaten apples.

Sample Input 1

1 2 2 2 1
2 4
5 1
3

Sample Output 1

12

The maximum possible sum of the deliciousness of the eaten apples can be achieved as follows:

Eat the 2-nd red apple.

Eat the 1-st green apple.

Paint the 1-st colorless apple green and eat it.

Sample Input 2

2 2 2 2 2
8 6
9 1
2 1

Sample Output 2

25

Sample Input 3

2 2 4 4 4
11 12 13 14
21 22 23 24
1 2 3 4

Sample Output 3

74

Solution in Haskell (GHC 7.10.3) (judge verdict: Runtime Error)

module Main where

import           Debug.Trace
import qualified Data.Vector.Unboxed           as VU
import           Data.List
import qualified Data.ByteString               as BS
import qualified Data.ByteString.Char8         as BSC8
import           Data.Char


getVUIntFromInputLineAtBSC8 :: IO (VU.Vector Int)
getVUIntFromInputLineAtBSC8 =
    VU.unfoldr (BSC8.readInt . BSC8.dropWhile isSpace) <$> BSC8.getLine
getListIntFromInputLineAtBSC8 =
    unfoldr (BSC8.readInt . BSC8.dropWhile isSpace) <$> BSC8.getLine
main :: IO ()
main = do
    [aX, aY, aA, aB, aC] <- getListIntFromInputLineAtBSC8
    aP                   <- getVUIntFromInputLineAtBSC8
    aQ                   <- getVUIntFromInputLineAtBSC8
    aR                   <- getVUIntFromInputLineAtBSC8

    putStrLn $ show
        (sumApple
            (VU.fromList (reverse (0:(sortConved (VU.toList aP) aX))))
            (VU.fromList (reverse (0:(sortConved (VU.toList aQ) aY))))
            (VU.fromList (reverse (0:(sortConved (VU.toList aR) (aX + aY)))))
            aX
            aY
            0
        )


sortConved :: [Int] -> Int -> [Int]
sortConved _        0 = []
sortConved []       _ = []
sortConved (x : []) 1 = [x]
sortConved (x : xs) c = if lgteq == c
    then (sortConved gteq (c))
    else if lgteq > c
        then (sortConved gteq c)
        else if lgteq == (c+1)
            then [x] ++ (sortConved gteq lgteq)
            else (sortConved lt (c - lgteq)) ++ [x] ++ (sortConved gteq lgteq)
  where
    lt    = filter (\y -> y <= x) xs
    gteq  = filter (\y -> y > x) xs
    lgteq = length gteq

sortMerged :: [(Int, Int)] -> [(Int, Int)]
sortMerged []       = []
sortMerged (x : xs) = (sortMerged lt) ++ [x] ++ (sortMerged gteq)
  where
    lt   = filter (\y -> (fst y) <= (fst x)) xs
    gteq = filter (\y -> (fst y) > (fst x)) xs



sumApple
    :: VU.Vector Int
    -> VU.Vector Int
    -> VU.Vector Int
    -> Int
    -> Int
    -> Int
    -> Int
sumApple reds greens nils tX tY tZ
    | (tX + tY) == tZ = 0
    | otherwise = if (maxNum == red) && (tX > 0)
        then red + (sumApple (VU.tail reds) greens nils (tX - 1) tY tZ)
        else if ((max green nil) == green) && (tY > 0)
            then green + (sumApple reds (VU.tail greens) nils tX (tY - 1) tZ)
            else nil + (sumApple reds greens (VU.tail nils) tX tY (tZ + 1))

  where
    red    = VU.head reds
    green  = VU.head greens
    nil    = VU.head nils
    maxNum = max red (max green nil)