Moving Piece

AtCoder

IDabc175_d

Time3000ms

Memory256MB

Difficulty—

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: $N$ $K$ $P_1$ $P_2$ $\cdots$ $P_N$ $C_1$ $C_2$ $\cdots$ $C_N$ [samples]

Samples

Input #1

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

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 $8$.

Input #2

2 3
2 1
10 -7

Output #2

Input #3

3 3
3 1 2
-1000 -2000 -3000

Output #3

\-1000

We have to make at least one move.

Input #4

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

Output #4

29507023469

The absolute value of the answer may be enormous.

API Response (JSON)

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    "name": "Moving Piece",
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      "content": "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",
      "description_type": "Markdown"
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    {
      "statement_type": "Markdown",
      "content": "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...",
      "is_translate": false,
      "language": "English"
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