You are given an integer array receiver of length n and an integer k. n players are playing a ball-passing game.
You choose the starting player, i. The game proceeds as follows: player i passes the ball to player receiver[i], who then passes it to receiver[receiver[i]], and so on, for k passes in total. The game's score is the sum of the indices of the players who touched the ball, including repetitions, i.e. i + receiver[i] + receiver[receiver[i]] + ... + receiver(k)[i].
Return the maximum possible score.
Notes:
receiver may contain duplicates.receiver[i] may be equal to i.
Example 1:
Input: receiver = [2,0,1], k = 4
Output: 6
Explanation:
Starting with player i = 2 the initial score is 2:
| Pass | Sender Index | Receiver Index | Score |
|---|---|---|---|
| 1 | 2 | 1 | 3 |
| 2 | 1 | 0 | 3 |
| 3 | 0 | 2 | 5 |
| 4 | 2 | 1 | 6 |
Example 2:
Input: receiver = [1,1,1,2,3], k = 3
Output: 10
Explanation:
Starting with player i = 4 the initial score is 4:
| Pass | Sender Index | Receiver Index | Score |
|---|---|---|---|
| 1 | 4 | 3 | 7 |
| 2 | 3 | 2 | 9 |
| 3 | 2 | 1 | 10 |
Constraints:
1 <= receiver.length == n <= 1050 <= receiver[i] <= n - 11 <= k <= 1010