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, MultiWayIf, TupleSections, TypeApplications #-}
{-# OPTIONS_GHC -O2 #-}


import Control.Arrow
import Control.Concurrent
import Control.Monad
import qualified Data.ByteString.Builder as B
import qualified Data.ByteString.Char8 as C
import Data.Bits
import Data.Complex
import Data.Char
import Data.Function
import Data.Function.HT
import qualified Data.IntMap.Strict as IM
import qualified Data.IntSet as IS
import Data.List
import Data.Monoid
import Data.Ord
import qualified Data.Sequence as Sq
import Data.Vector.Algorithms.Search
import qualified Data.Vector as V
import qualified Data.Vector.Mutable as VM
import qualified Data.Vector.Unboxed as U
import qualified Data.Vector.Unboxed.Mutable as UM
import Debug.Trace
import System.IO

r :: Int -> IO (U.Vector Int)
r n = U.unfoldrN n (C.readInt . C.dropWhile (==' ')) <$> C.getLine

r' :: IO [Int]
r'  =   unfoldr    (C.readInt . C.dropWhile (==' ')) <$> C.getLine

d :: Int -> Int -> Double
d x y = fromIntegral x / fromIntegral y


data LoopK = L {lenL :: Int, sumL :: Integer, remC :: Integer, fremC :: Integer}

lpB :: (Int,Integer,Integer,Integer) -> LoopK
lpB (a,b,c,d) = L a b c d

main = do
    [n,k] <- r' :: IO [Int]
    ps <- U.map pred <$> r n
    cs <- V.fromList <$> map fromIntegral <$> r'
    visited <- UM.replicate n False
    loops <- filter (/=[]) <$> (mapM (\f -> findloop f ps cs visited) [0..n-1])
    let sums = map sum loops
    let remCs = map (optForLoop k) loops
    let fremCs = map (fullOptForLoop k) loops
    -- print $ loops
    -- print $ sums
    -- print $ remCs
    -- print $ fremCs
    print $ maximum $ map ((re k).lpB) $ zip4 (map length loops) sums remCs fremCs

findloop :: Int -> U.Vector Int -> V.Vector Integer -> UM.IOVector Bool -> IO [Integer]
findloop from ps cs visited = do
    x <- UM.read visited from
    if x then return [] else do
        let resP = (from :) $ takeWhile (/= from) $ tail $ iterate (ps U.!) from
        mapM_ (\a -> UM.write visited a True) resP
        return $ map (\p -> cs V.! p) resP

optForLoop :: Int -> [Integer] ->  Integer
optForLoop k lp = let remK = k `rem` length lp in
    if remK == 0 then 0 else maximum $ map (kukan lp) [1..remK]

fullOptForLoop :: Int -> [Integer] -> Integer
fullOptForLoop k lp = maximum $ map (kukan lp) [1..min k (length lp)]



kukan :: [Integer] -> Int -> Integer
kukan lp len = maximum $ zipWith (-) (drop len (scanl1 (+) (cycle lp))) (scanl1 (+) lp)

re :: Int -> LoopK -> Integer
re k l = if sumL l > 0 then max ((floor $ d k (lenL l)) * sumL l + remC l) ((pred $ floor $ d k (lenL l)) * sumL l + fremC l) else fremC l