You are given a $0$ indexed integer array receiver of length $n$ and an integer k.

There are $n$ players numbered from $0$ to $n - 1$ taking part in a ball passing game. When a player x holds the ball, they pass it directly to player receiver[x].

The game starts by selecting any player i ($0 \le i < n$) to hold the ball initially, which sets the starting score to i. The ball is then passed exactly k times. Whenever the ball is passed to player receiver[x], the value receiver[x] is added to the current score.

Return the maximum possible score achievable after k passes by choosing the optimal starting player.

Constraints:

• $1 \le$ receiver.length $== n \le 10^5$

• $0 \le$ receiver[i] $\le n - 1$

• $1 \le$ k $\le 10^{10}$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.