Buggy python submission (verdict: Time Limit Exceeded):
#!/usr/bin/env python3

import sys
from typing import Any, Callable, Deque, Dict, List, Mapping, Optional, Sequence, Set, Tuple, TypeVar, Union
# import time
# import math, cmath
# import numpy as np
# import scipy.sparse.csgraph as cs            # csgraph_from_dense(ndarray, null_value=inf), bellman_ford(G, return_predecessors=True), dijkstra, floyd_warshall
# import random                                # random, uniform, randint, randrange, shuffle, sample
# import string                                # ascii_lowercase, ascii_uppercase, ascii_letters, digits, hexdigits
# import re                                    # re.compile(pattern) => ptn obj; p.search(s), p.match(s), p.finditer(s) => match obj; p.sub(after, s)
# from bisect import bisect_left, bisect_right # bisect_left(a, x, lo=0, hi=len(a)) returns i such that all(val<x for val in a[lo:i]) and all(val>-=x for val in a[i:hi]).
# from collections import deque                # deque class. deque(L): dq.append(x), dq.appendleft(x), dq.pop(), dq.popleft(), dq.rotate()
# from collections import defaultdict          # subclass of dict. defaultdict(facroty)
# from collections import Counter              # subclass of dict. Counter(iter): c.elements(), c.most_common(n), c.subtract(iter)
# from datetime import date, datetime          # date.today(), date(year,month,day) => date obj; datetime.now(), datetime(year,month,day,hour,second,microsecond) => datetime obj; subtraction => timedelta obj
# from datetime.datetime import strptime       # strptime('2019/01/01 10:05:20', '%Y/%m/%d/ %H:%M:%S') returns datetime obj
# from datetime import timedelta               # td.days, td.seconds, td.microseconds, td.total_seconds(). abs function is also available.
# from copy import copy, deepcopy              # use deepcopy to copy multi-dimentional matrix without reference
# from functools import reduce                 # reduce(f, iter[, init])
# from functools import lru_cache              # @lrucache ...arguments of functions should be able to be keys of dict (e.g. list is not allowed)
# from heapq import heapify, heappush, heappop # built-in list. heapify(L) changes list in-place to min-heap in O(n), heappush(heapL, x) and heappop(heapL) in O(lgn).
# from heapq import _heapify_max, _heappop_max, _siftdown_max
# from heapq import nlargest, nsmallest        # nlargest(n, iter[, key]) returns k-largest-list in O(n+klgn).
# from itertools import count, cycle, repeat   # count(start[,step]), cycle(iter), repeat(elm[,n])
# from itertools import groupby                # [(k, list(g)) for k, g in groupby('000112')] returns [('0',['0','0','0']), ('1',['1','1']), ('2',['2'])]
# from itertools import starmap                # starmap(pow, [[2,5], [3,2]]) returns [32, 9]
# from itertools import product, permutations  # product(iter, repeat=n), permutations(iter[,r])
# from itertools import combinations, combinations_with_replacement
# from itertools import accumulate             # accumulate(iter[, f])
# from operator import itemgetter              # itemgetter(1), itemgetter('key')
# from fractions import Fraction               # Fraction(a, b) => a / b ∈ Q. note: Fraction(0.1) do not returns Fraciton(1, 10). Fraction('0.1') returns Fraction(1, 10)



def main():
    Num = Union[int, float]
    mod = 1000000007                # 10^9+7
    inf = float('inf')              # sys.float_info.max = 1.79e+308
    # inf = 2 ** 63 - 1             # (for fast JIT compile in PyPy) 9.22e+18
    sys.setrecursionlimit(10**6)    # 1000 -> 1000000
    def input():  return sys.stdin.readline().rstrip()
    def ii():     return int(input())
    def isp():    return input().split()
    def mi():     return map(int, input().split())
    def mi_0():   return map(lambda x: int(x)-1, input().split())
    def lmi():    return list(map(int, input().split()))
    def lmi_0():  return list(map(lambda x: int(x)-1, input().split()))
    def li():     return list(input())
    def debug(x): print(x, file=sys.stderr)
    # def _heappush_max(h, item): h.append(item); _siftdown_max(h, 0, len(h)-1)


    def calc_score(start):
        order = [None] * n
        accum = [None] * n
        order[start] = 0
        accum[start] = 0
        place = start
        cnt = 0
        current_score = 0
        M = -inf

        while cnt < k:
            place = P[place]    # 移動
            cnt += 1    # 移動回数
            current_score += C[place]    # 移動後の index でスコアに追加
            M = max(M, current_score)    # [スタートの次点, 現在地] まで任意の場所をゴールに選ぶときのスコア最大値
            if order[place] is None:
                # 未訪問
                order[place] = cnt
                accum[place] = current_score
            else:
                # 訪問ずみ。loop
                head_len = order[place]
                loop_len = cnt - head_len
                head_score = accum[place]
                loop_gain = current_score - accum[place]
                if loop_gain <= 0:
                    # debug('encountered loop, but non-positive loop.')
                    return M
                else:
                    # debug('encountered positive loop.')
                    loop_times, res = divmod(k - head_len, loop_len)
                    # place からスタートして "0 以上" res 以下だけ進むときの
                    res_score = 0    # 稼ぐ最大スコア
                    tmp_score = 0    # 現在の累積スコア
                    tmp_place = place    # 現在地
                    for i in range(res):
                        tmp_place = P[tmp_place]
                        tmp_score += C[tmp_place]    # 移動後の index でスコアに追加
                        res_score = max(res_score, tmp_score)
                    loop_score = head_score + loop_times * loop_gain + res_score
                    return loop_score

        # debug('never encountered loop.')
        return M
            

    n, k = mi()
    P = lmi_0()
    C = lmi()

    ans = -inf
    for i in range(n):
        # debug(ans)
        ans = max(ans, calc_score(i))
    print(ans)


if __name__ == "__main__":
    main()


Fixed submission:
#!/usr/bin/env python3

import sys


def main():
    # inf = float('inf')              # sys.float_info.max = 1.79e+308
    inf = 2 ** 63 - 1             # (for fast JIT compile in PyPy) 9.22e+18
    sys.setrecursionlimit(10**6)    # 1000 -> 1000000
    def input():  return sys.stdin.readline().rstrip()
    def ii():     return int(input())
    def isp():    return input().split()
    def mi():     return map(int, input().split())
    def mi_0():   return map(lambda x: int(x)-1, input().split())
    def lmi():    return list(map(int, input().split()))
    def lmi_0():  return list(map(lambda x: int(x)-1, input().split()))
    def li():     return list(input())
    def debug(x): print(x, file=sys.stderr)



    def calc_score(start):
        order = [None] * n
        accum = [None] * n
        order[start] = 0
        accum[start] = 0
        place = start
        cnt = 0
        current_score = 0
        M = -inf

        while cnt < k:
            place = P[place]    # 移動
            cnt += 1    # 移動回数
            current_score += C[place]    # 移動後の index でスコアに追加
            M = max(M, current_score)    # [スタートの次点, 現在地] まで任意の場所をゴールに選ぶときのスコア最大値
            if order[place] is None:
                # 未訪問
                order[place] = cnt
                accum[place] = current_score
            else:
                # 訪問ずみ (loop)
                head_len = order[place]
                loop_len = cnt - head_len
                head_score = accum[place]
                loop_gain = current_score - accum[place]
                if loop_gain <= 0:
                    # debug('encountered loop, but non-positive loop.')
                    return M
                else:
                    # debug('encountered positive loop.')
                    loop_times, res = divmod(k - head_len, loop_len)
                    # place からスタートして "0 以上" res 以下だけ進むときの
                    res_score = 0    # 稼ぐ最大スコア
                    tmp_score = 0    # 現在の累積スコア
                    tmp_place = place    # 現在地
                    for _ in range(res):
                        tmp_place = P[tmp_place]
                        tmp_score += C[tmp_place]    # 移動後の index でスコアに追加
                        res_score = max(res_score, tmp_score)
                    # 限界まで loop を回した上で 0 ~ res だけ貪欲に稼ぐ vs 限界 - 1 回 loop を回し確実にもう一回好きなところでとめられるようにして稼ぐ
                    loop_score = head_score + loop_times * loop_gain + res_score
                    stop_score = M + (loop_times - 1) * loop_gain
                    return max(loop_score, stop_score)

        # debug('never encountered loop.')
        return M
            

    n, k = mi()
    P = lmi_0()
    C = lmi()

    ans = -inf
    for i in range(n):
        score = calc_score(i)
        # debug(f'start: {i} ans: {score}')
        ans = max(ans, score)
    print(ans)


if __name__ == "__main__":
    main()