Problem:
Score : 400 points

Problem Statement

Takahashi will play a game using a piece on an array of squares numbered 1, 2, \cdots, N. Square i has an integer C_i written on it. Also, he is given a permutation of 1, 2, \cdots, N: P_1, P_2, \cdots, P_N.

Now, he will choose one square and place the piece on that square. Then, he will make the following move some number of times between 1 and K (inclusive):

In one move, if the piece is now on Square i (1 \leq i \leq N), move it to Square P_i. Here, his score increases by C_{P_i}.

Help him by finding the maximum possible score at the end of the game. (The score is 0 at the beginning of the game.)

Constraints

2 \leq N \leq 5000

1 \leq K \leq 10^9

1 \leq P_i \leq N

P_i \neq i

P_1, P_2, \cdots, P_N are all different.

-10^9 \leq C_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
P_1 P_2 \cdots P_N
C_1 C_2 \cdots C_N

Output

Print the maximum possible score at the end of the game.

Sample Input 1

5 2
2 4 5 1 3
3 4 -10 -8 8

Sample Output 1

8

When we start at some square of our choice and make at most two moves, we have the following options:

If we start at Square 1, making one move sends the piece to Square 2, after which the score is 4. Making another move sends the piece to Square 4, after which the score is 4 + (-8) = -4.

If we start at Square 2, making one move sends the piece to Square 4, after which the score is -8. Making another move sends the piece to Square 1, after which the score is -8 + 3 = -5.

If we start at Square 3, making one move sends the piece to Square 5, after which the score is 8. Making another move sends the piece to Square 3, after which the score is 8 + (-10) = -2.

If we start at Square 4, making one move sends the piece to Square 1, after which the score is 3. Making another move sends the piece to Square 2, after which the score is 3 + 4 = 7.

If we start at Square 5, making one move sends the piece to Square 3, after which the score is -10. Making another move sends the piece to Square 5, after which the score is -10 + 8 = -2.

The maximum score achieved is 8.

Sample Input 2

2 3
2 1
10 -7

Sample Output 2

13

Sample Input 3

3 3
3 1 2
-1000 -2000 -3000

Sample Output 3

-1000

We have to make at least one move.

Sample Input 4

10 58
9 1 6 7 8 4 3 2 10 5
695279662 988782657 -119067776 382975538 -151885171 -177220596 -169777795 37619092 389386780 980092719

Sample Output 4

29507023469

The absolute value of the answer may be enormous.

Solution in Haskell (GHC 8.8.3) (judge verdict: Time Limit Exceeded)

--{-# LANGUAGE BangPatterns #-}
--{-# LANGUAGE ScopedTypeVariables #-}
--{-# LANGUAGE FlexibleContexts #-}
--{-# LANGUAGE ViewPatterns #-}
--{-# LANGUAGE OverloadedStrings #-}
--{-# LANGUAGE Strict #-}
--{-# LANGUAGE NumericUnderscores #-}
--{-# LANGUAGE BlockArguments #-}
{-# LANGUAGE MultiWayIf #-}

import qualified Data.Vector as V
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM
import qualified Data.ByteString.Char8 as BC
import qualified Data.Map.Strict as MPS
import qualified Data.Map as MP
import qualified Data.Set as ST
import qualified Data.Sequence as SQ
import Data.Array
import Data.Array.Unboxed
import Data.Array.ST
import Data.Array.IO
import Data.Maybe
import Data.Ord
import Data.Ratio
import Data.Char
import Data.Bits
import Data.List
import Data.Tuple
import Data.Functor
import Data.IORef
import Data.STRef
import Control.Applicative
import Control.Monad
import Control.Monad.ST
import Control.Monad.State.Strict
import Debug.Trace
import qualified Data.OrdPSQ as PSQ
import qualified Data.Vector.Algorithms.Merge as VAM
import qualified Data.Heap as HP
import Numeric.Extra
import Data.Tuple.Extra
import Data.List.Extra

data OrdQ = Ascending | Descending

--------------------------------------------------------------------------
simulate :: VU.Vector Int -> VU.Vector Int -> Int -> Int -> Int -> ST.Set Int -> ST.Set Int
simulate ps cs i k acc st
    | k == 0 = st
    | otherwise  = simulate ps cs nexti (k-1) (acc+point) st'
    where
        nexti = ps VU.! i
        point = cs VU.! nexti
        st' = ST.insert (acc+point) st

main = do
    [n, k] <- sLineToIntL
    ps <- VU.map m1 <$> sLineToIntV n
    cs <- sLineToIntV n
    let base = VU.maximum cs
    res <- flip evalStateT base $ do
        forM_ [0..n-1] $ \i -> do
            let res = simulate ps cs i k 0 ST.empty
            modify' (max (ST.findMax res))
        get
    print res
--------------------------------------------------------------------------

-- Input Util
int :: IO Int
int = bsToInt <$> BC.getLine

double :: IO Double
double = bsToDouble <$> BC.getLine

str :: IO String
str = BC.unpack <$> BC.getLine

strBS :: IO BC.ByteString
strBS = BC.getLine

-- convert
bsToInt :: BC.ByteString -> Int
bsToInt = fst . fromJust . BC.readInt

bsToDouble :: BC.ByteString -> Double
bsToDouble = read . BC.unpack

bsToIntTuple :: BC.ByteString -> (Int, Int)
bsToIntTuple bs = (a,b)
    where
        Just (a,bs') = parseInt bs
        Just (b,_) = parseInt bs'

bsToIntTriple :: BC.ByteString -> (Int, Int, Int)
bsToIntTriple bs = (a,b,c)
    where
        Just (a,bs') = parseInt bs
        Just (b,bs'') = parseInt bs'
        Just (c,_) = parseInt bs''

parseInt :: BC.ByteString -> Maybe (Int, BC.ByteString)
parseInt = BC.readInt . BC.dropWhile isSpace

-- single line
fromSLineL :: (BC.ByteString -> a) -> IO [a]
fromSLineL f =  map f . BC.words <$> strBS

-- from single line to List / VU.Vector
sLineToIntL :: IO [Int]
sLineToIntL = fromSLineL bsToInt

sLineToDoubleL :: IO [Double]
sLineToDoubleL = fromSLineL bsToDouble

sLineToStrL :: IO [String]
sLineToStrL = fromSLineL BC.unpack

sLineToStrBSL :: IO [BC.ByteString]
sLineToStrBSL = fromSLineL id

sLineToIntV :: Int -> IO (VU.Vector Int)
sLineToIntV n = VU.unfoldrN n parseInt <$> BC.getLine

sLineToDoubleV :: IO (VU.Vector Double)
sLineToDoubleV = VU.fromList . map bsToDouble . BC.words <$> BC.getLine

-- multiple lines
fromMLinesL :: Int -> (BC.ByteString -> a) -> IO [a]
fromMLinesL n f = replicateM n (f <$> strBS)

fromMLinesV :: VU.Unbox a => Int -> (BC.ByteString -> a) -> IO (VU.Vector a)
fromMLinesV n f = VU.replicateM n (f <$> strBS)

-- from multiple lines to List / VU.Vector
mLinesToIntL :: Int -> IO [Int]
mLinesToIntL n = fromMLinesL n bsToInt

mLinesToDoubleL :: Int -> IO [Double]
mLinesToDoubleL n = fromMLinesL n bsToDouble

mLinesToStrL :: Int -> IO [String]
mLinesToStrL n = fromMLinesL n BC.unpack

mLinesToStrBSL :: Int -> IO [BC.ByteString]
mLinesToStrBSL n = fromMLinesL n id

mLinesToTupleL :: Int -> IO [(Int, Int)]
mLinesToTupleL n = fromMLinesL n bsToIntTuple

mLinesToTripleL :: Int -> IO [(Int, Int, Int)]
mLinesToTripleL n = fromMLinesL n bsToIntTriple

mLinesToIntV :: Int -> IO (VU.Vector Int)
mLinesToIntV n = fromMLinesV n bsToInt

mLinesToDoubleV :: Int -> IO (VU.Vector Double)
mLinesToDoubleV n = fromMLinesV n bsToDouble

mLinesToTupleV :: Int -> IO (VU.Vector (Int, Int))
mLinesToTupleV n = fromMLinesV n bsToIntTuple

mLinesToTripleV :: Int -> IO (VU.Vector (Int, Int, Int))
mLinesToTripleV n = fromMLinesV n bsToIntTriple

-- output
yesnoL :: Bool -> IO ()
yesnoL cond
    | cond = putStrLn "Yes"
    | otherwise = putStrLn "No"

yesnoU :: Bool -> IO ()
yesnoU cond
    | cond = putStrLn "YES"
    | otherwise = putStrLn "NO"

-- others
strToChr :: String -> Char
strToChr [x] = x

chrToStr :: Char -> String
chrToStr x = [x]

m1 :: Int -> Int
m1 = subtract 1

toDouble :: Int -> Double
toDouble = fromIntegral

toInt :: Double -> Int
toInt = floor

sqToList :: SQ.Seq a -> [a]
sqToList sq =
    case SQ.viewl sq of
        l SQ.:< sq' -> l : sqToList sq'
        SQ.EmptyL -> []

sortV :: (Ord a, VU.Unbox a) => VU.Vector a -> VU.Vector a
sortV v = VU.create $ do
    w <- VU.thaw v
    VAM.sort w
    return w


sortVR :: (Ord a, VU.Unbox a) => VU.Vector a -> VU.Vector a
sortVR v = VU.create $ do
    w <- VU.thaw v
    VAM.sortBy (flip compare) w
    return w

buildPQL :: Ord a => OrdQ -> [a] -> PSQ.OrdPSQ Int Int a
buildPQL oq xs =
    case oq of
        Ascending -> f $ zip3 [1..l] [1..l] $ sort xs
        Descending -> f $ zip3  [1..l] (map negate [1..l]) $ sort xs
    where
        l = length xs
        f = foldl' g PSQ.empty
        g acc (k,p,v) = PSQ.insert k p v acc

buildPQV :: (Ord a, VU.Unbox a) => OrdQ -> VU.Vector a -> PSQ.OrdPSQ Int Int a
buildPQV oq xs =
    case oq of
        Ascending -> f $ VU.zip3 (VU.generate l (+1)) (VU.generate l (+1)) $ sortV xs
        Descending -> f $ VU.zip3  (VU.generate l (+1)) (VU.generate l $ negate . (+1)) $ sortV xs
    where
        l = VU.length xs
        f = VU.foldl' g PSQ.empty
        g acc (k,p,v) = PSQ.insert k p v acc