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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

import sys
input = sys.stdin.readline
# sys.setrecursionlimit(100000)


def main():
    n, k = [int(i) for i in input().strip().split()]
    P = [None] + [int(i) for i in input().strip().split()]
    C = [None] + [int(i) for i in input().strip().split()]
    seen = set()
    loops = []
    score = []
    loop_sums = []
    loop_max = []
    ans = -float("inf")
    if max(C[1:]) < 0:
        ans = max(C[1:])
        print(ans)
        return

    # ループを探す
    for i in range(1, n + 1):
        flag = False
        loop = []
        sc = []
        _sum = 0
        j = i
        if j not in seen:
            flag = True
            while j not in loop:
                loop.append((j))
                sc.append(C[j])
                seen.add(j)
                _sum += C[j]
                j = P[j]
        if flag:
            loops.append(loop)
            loop_sums.append(_sum)
            score.append(sc)

    # 各ループで作れる最大値を出す
    _max = []
    for i in range(len(loops)):
        loop = loops[i]
        sc = score[i]
        _max = -float("inf")
        # 各始点からループを始める
        for j in range(len(loop)):
            # 1周してみる
            _tmp = 0
            for p in range(min(len(loop), k)):  # 進める歩数はループの回数とkの小さい方
                ptr = (j + p) % len(loop)
                _tmp += sc[ptr]
                _max = max(_max, _tmp)

        # そのループの最大値を記録する
        loop_max.append(_max)

    """
    print("loops", loops)
    print("score", score)
    print("loop_sums", loop_sums)
    print("loop_max", loop_max)
    """

    # 各ループについて評価する
    for i in range(len(loops)):
        loop = loops[i]
        sc = score[i]
        _sum = loop_sums[i]  # ループの合計値
        _max = loop_max[i]  # 周回せずにループで得られる最大値

        # 周回しない場合
        ans = max(ans, _max)

        # 周回する場合
        loop_sum = _sum * (k // (len(loop)))
        ans = max(ans, loop_sum)
        res = k % len(loop)

        # 各始点からループを始める
        if res > 0:
            _res_max = -float("inf")
            for j in range(len(loop)):
                # 1周してみる
                _tmp = 0
                # 残ってるホップ回数で作れる最大値を探す
                for p in range(res):
                    ptr = (j + p) % len(loop)
                    _tmp += sc[ptr]
                    _res_max = max(_res_max, _tmp)
            ans = max(ans, loop_sum + _res_max)
    print(ans)
    return


if __name__ == "__main__":
    main()