<p>You are given an integer array <code>receiver</code> of length <code>n</code> and an integer <code>k</code>. <code>n</code> players are playing a ball-passing game.</p>

<p>You choose the starting player, <code>i</code>. The game proceeds as follows: player <code>i</code> passes the ball to player <code>receiver[i]</code>, who then passes it to <code>receiver[receiver[i]]</code>, and so on, for <code>k</code> passes in total. The game&#39;s score is the sum of the indices of the players who touched the ball, including repetitions, i.e. <code>i + receiver[i] + receiver[receiver[i]] + ... + receiver<sup>(k)</sup>[i]</code>.</p>

<p>Return&nbsp;the <strong>maximum</strong>&nbsp;possible score.</p>

<p><strong>Notes:</strong></p>

<ul>
	<li><code>receiver</code> may contain duplicates.</li>
	<li><code>receiver[i]</code> may be equal to <code>i</code>.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">receiver = [2,0,1], k = 4</span></p>

<p><strong>Output:</strong> <span class="example-io">6</span></p>

<p><strong>Explanation:</strong></p>

<p>Starting with player <code>i = 2</code> the initial score is 2:</p>

<table>
	<tbody>
		<tr>
			<th>Pass</th>
			<th>Sender Index</th>
			<th>Receiver Index</th>
			<th>Score</th>
		</tr>
		<tr>
			<td>1</td>
			<td>2</td>
			<td>1</td>
			<td>3</td>
		</tr>
		<tr>
			<td>2</td>
			<td>1</td>
			<td>0</td>
			<td>3</td>
		</tr>
		<tr>
			<td>3</td>
			<td>0</td>
			<td>2</td>
			<td>5</td>
		</tr>
		<tr>
			<td>4</td>
			<td>2</td>
			<td>1</td>
			<td>6</td>
		</tr>
	</tbody>
</table>
</div>

<p><strong class="example">Example 2:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">receiver = [1,1,1,2,3], k = 3</span></p>

<p><strong>Output:</strong> <span class="example-io">10</span></p>

<p><strong>Explanation:</strong></p>

<p>Starting with player <code>i = 4</code> the initial score is 4:</p>

<table>
	<tbody>
		<tr>
			<th>Pass</th>
			<th>Sender Index</th>
			<th>Receiver Index</th>
			<th>Score</th>
		</tr>
		<tr>
			<td>1</td>
			<td>4</td>
			<td>3</td>
			<td>7</td>
		</tr>
		<tr>
			<td>2</td>
			<td>3</td>
			<td>2</td>
			<td>9</td>
		</tr>
		<tr>
			<td>3</td>
			<td>2</td>
			<td>1</td>
			<td>10</td>
		</tr>
	</tbody>
</table>
</div>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= receiver.length == n &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= receiver[i] &lt;= n - 1</code></li>
	<li><code>1 &lt;= k &lt;= 10<sup>10</sup></code></li>
</ul>

class Solution:
    def getMaxFunctionValue(self, receiver: List[int], k: int) -> int:
        n = len(receiver)
        dists = [receiver]  # distance for [2**0 = 1] step from idx
        scores = [receiver]  # score for the jump from idx
        for _ in f"{k:b}":
            scores.append([scores[-1][i] + scores[-1][dists[-1][i]] for i in range(n)])
            dists.append([dists[-1][dists[-1][i]] for i in range(n)])

        max_score = 0
        for i in range(n):
            score = curr = i
            for pwd, b in enumerate(reversed(f"{k:b}")):
                if b == '1':
                    score += scores[pwd][curr]
                    curr = dists[pwd][curr]
            max_score = max(max_score, score)
        return max_score
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