"content":"<p>You are given a <strong>0-indexed</strong> integer array <code>receiver</code> of length <code>n</code> and an integer <code>k</code>.</p>\n\n<p>There are <code>n</code> players having a <strong>unique id</strong> in the range <code>[0, n - 1]</code> who will play a ball passing game, and <code>receiver[i]</code> is the id of the player who receives passes from the player with id <code>i</code>. Players can pass to themselves, <strong>i.e.</strong> <code>receiver[i]</code> may be equal to <code>i</code>.</p>\n\n<p>You must choose one of the <code>n</code> players as the starting player for the game, and the ball will be passed <strong>exactly</strong> <code>k</code> times starting from the chosen player.</p>\n\n<p>For a chosen starting player having id <code>x</code>, we define a function <code>f(x)</code> that denotes the <strong>sum</strong> of <code>x</code> and the <strong>ids</strong> of all players who receive the ball during the <code>k</code> passes, <strong>including repetitions</strong>. In other words, <code>f(x) = x + receiver[x] + receiver[receiver[x]] + ... + receiver<sup>(k)</sup>[x]</code>.</p>\n\n<p>Your task is to choose a starting player having id <code>x</code> that <strong>maximizes</strong> the value of <code>f(x)</code>.</p>\n\n<p>Return <em>an integer denoting the <strong>maximum</strong> value of the function.</em></p>\n\n<p><strong>Note:</strong> <code>receiver</code> may contain duplicates.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<table border=\"1\" cellspacing=\"3\" style=\"border-collapse: separate; text-align: center;\">\n\t<tbody>\n\t\t<tr>\n\t\t\t<th style=\"padding: 5px; border: 1px solid black;\">Pass Number</th>\n\t\t\t<th style=\"padding: 5px; border: 1px solid black;\">Sender ID</th>\n\t\t\t<th style=\"padding: 5px; border: 1px solid black;\">Receiver ID</th>\n\t\t\t<th style=\"padding: 5px; border: 1px solid black;\">x + Receiver IDs</th>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td style=\"padding: 5px; border: 1px solid black;\"> </td>\n\t\t\t<td style=\"padding: 5px; border: 1px solid black;\"> </td>\n\t\t\t<td style=\"padding: 5px; border: 1px solid black;\"> </td>\n\t\t\t<td style=\"padding: 5px; border: 1px solid black;\">2</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td style=\"padding: 5px; border: 1px solid black;\">1</td>\n\t\t\t<td style=\"padding: 5px; border: 1px solid black;\">2</td>\n\t\t\t<td style=\"padding: 5px; border: 1px solid black;\">1</td>\n\t\t\t<td style=\"padding: 5px; border: 1px solid black;\">3</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td style=\"padding: 5px; border: 1px solid black;\">2</td>\n\t\t\t<td style=\"padding: 5px; border: 1px solid black;\">1</td>\n\t\t\t<td style=\"padding: 5px; border: 1px solid black;\">0</td>\n\t\t\t<td style=\"padding: 5px; border: 1px solid black;\">3</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td style=\"padding: 5px; border: 1px solid black;\">3</td>\n\t\t\t<td style=\"padding: 5px; border: 1px solid black;\">0</td>\n\t\t\t<td style=\"padding: 5px; border: 1px solid black;\">2</td>\n\t\t\t<td style=\"padding: 5px; border: 1px solid black;\">5</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td style=\"padding: 5px; border: 1px solid black;\">4</td>\n\t\t\t<td style=\"padding: 5px; border: 1px solid black;\">2</td>\n\t\t\t<td style=\"padding: 5px; border: 1px solid black;\">1</td>\n\t\t\t<td style=\"padding: 5px; border: 1px solid black;\">6</td>\n\t\t</tr>\n\t</tbody>\n</table>\n\n<pre>\n<strong>Input:</strong> receiver = [2,0,1], k = 4\n<strong>Output:</strong> 6\n<strong>Explanation:</strong> The table above shows a simulation of the game starting with the player having id x = 2. \nFrom the table, f(2) is equal to 6. \nIt can be shown that 6 is the maximum achievable value of the function. \nHence, the output is 6. \n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<table border=\"1\" cellspacing=\"3\" style=\"border-collapse: separate; text-align: center;\">\n\t<tbody>\n\t\t<tr>\n\t\t\t<th style=\"padding: 5px; border: 1px solid black;\">Pass Number</th>\n\t\t\t<th style=\"p
"<div class=\"_1l1MA\">We can solve the problem using binary lifting.</div>",
"<div class=\"_1l1MA\">For each player with id <code>x</code> and for every <code>i</code> in the range <code>[0, ceil(log<sub>2</sub>k)]</code>, we can determine the last receiver's id and compute the sum of player ids who receive the ball after <code>2<sup>i</sup></code> passes, starting from <code>x</code>.</div>",
"<div class=\"_1l1MA\">Let <code>last_receiver[x][i] =</code> the last receiver's id after <code>2<sup>i</sup></code> passes, and <code>sum[x][i] =</code> the sum of player ids who receive the ball after <code>2<sup>i</sup></code> passes. For all <code>x</code> in the range <code>[0, n - 1]</code>, <code>last_receiver[x][0] = receiver[x]</code>, and <code>sum[x][0] = receiver[x]</code>.</div>",
"<div class=\"_1l1MA\">Then for <code>i</code> in range <code>[1, ceil(log<sub>2</sub>k)]</code>,<code>last_receiver[x][i] = last_receiver[last_receiver[x][i - 1]][i - 1]</code> and <code>sum[x][i] = sum[x][i - 1] + sum[last_receiver[x][i - 1]][i - 1]</code>, for all <code>x</code> in the range <code>[0, n - 1]</code>.</div>",
"<div class=\"_1l1MA\">Starting from each player id <code>x</code>, we can now go through the powers of <code>2</code> in the binary representation of <code>k</code> and make jumps corresponding to each power, using the pre-computed values, to compute <code>f(x)</code>.</div>",
"<div class=\"_1l1MA\">The answer is the maximum <code>f(x)</code> from each player id.</div>"
"envInfo":"{\"cpp\": [\"C++\", \"<p>Compiled with <code> clang 11 </code> using the latest C++ 20 standard.</p>\\r\\n\\r\\n<p>Your code is compiled with level two optimization (<code>-O2</code>). <a href=\\\"https://github.com/google/sanitizers/wiki/AddressSanitizer\\\" target=\\\"_blank\\\">AddressSanitizer</a> is also enabled to help detect out-of-bounds and use-after-free bugs.</p>\\r\\n\\r\\n<p>Most standard library headers are already included automatically for your convenience.</p>\"], \"java\": [\"Java\", \"<p><code>OpenJDK 17</code>. Java 8 features such as lambda expressions and stream API can be used. </p>\\r\\n\\r\\n<p>Most standard library headers are already included automatically for your convenience.</p>\\r\\n<p>Includes <code>Pair</code> class from https://docs.oracle.com/javase/8/javafx/api/javafx/util/Pair.html.</p>\"], \"python\": [\"Python\", \"<p><code>Python 2.7.12</code>.</p>\\r\\n\\r\\n<p>Most libraries are already imported automatically for your convenience, such as <a href=\\\"https://docs.python.org/2/library/array.html\\\" target=\\\"_blank\\\">array</a>, <a href=\\\"https://docs.python.org/2/library/bisect.html\\\" target=\\\"_blank\\\">bisect</a>, <a href=\\\"https://docs.python.org/2/library/collections.html\\\" target=\\\"_blank\\\">collections</a>. If you need more libraries, you can import it yourself.</p>\\r\\n\\r\\n<p>For Map/TreeMap data structure, you may use <a href=\\\"http://www.grantjenks.com/docs/sortedcontainers/\\\" target=\\\"_blank\\\">sortedcontainers</a> library.</p>\\r\\n\\r\\n<p>Note that Python 2.7 <a href=\\\"https://www.python.org/dev/peps/pep-0373/\\\" target=\\\"_blank\\\">will not be maintained past 2020</a>. For the latest Python, please choose Python3 instead.</p>\"], \"c\": [\"C\", \"<p>Compiled with <code>gcc 8.2</code> using the gnu11 standard.</p>\\r\\n\\r\\n<p>Your code is compiled with level one optimization (<code>-O1</code>). <a href=\\\"https://github.com/google/sanitizers/wiki/AddressSanitizer\\\" target=\\\"_blank\\\">AddressSanitizer</a> is also enabled to help detect out-of-bounds and use-after-free bugs.</p>\\r\\n\\r\\n<p>Most standard library headers are already included automatically for your convenience.</p>\\r\\n\\r\\n<p>For hash table operations, you may use <a href=\\\"https://troydhanson.github.io/uthash/\\\" target=\\\"_blank\\\">uthash</a>. \\\"uthash.h\\\" is included by default. Below are some examples:</p>\\r\\n\\r\\n<p><b>1. Adding an item to a hash.</b>\\r\\n<pre>\\r\\nstruct hash_entry {\\r\\n int id; /* we'll use this field as the key */\\r\\n char name[10];\\r\\n UT_hash_handle hh; /* makes this structure hashable */\\r\\n};\\r\\n\\r\\nstruct hash_entry *users = NULL;\\r\\n\\r\\nvoid add_user(struct hash_entry *s) {\\r\\n HASH_ADD_INT(users, id, s);\\r\\n}\\r\\n</pre>\\r\\n</p>\\r\\n\\r\\n<p><b>2. Looking up an item in a hash:</b>\\r\\n<pre>\\r\\nstruct hash_entry *find_user(int user_id) {\\r\\n struct hash_entry *s;\\r\\n HASH_FIND_INT(users, &user_id, s);\\r\\n return s;\\r\\n}\\r\\n</pre>\\r\\n</p>\\r\\n\\r\\n<p><b>3. Deleting an item in a hash:</b>\\r\\n<pre>\\r\\nvoid delete_user(struct hash_entry *user) {\\r\\n HASH_DEL(users, user); \\r\\n}\\r\\n</pre>\\r\\n</p>\"], \"csharp\": [\"C#\", \"<p><a href=\\\"https://learn.microsoft.com/en-us/dotnet/csharp/whats-new/csharp-10\\\" target=\\\"_blank\\\">C# 10 with .NET 6 runtime</a></p>\"], \"javascript\": [\"JavaScript\", \"<p><code>Node.js 16.13.2</code>.</p>\\r\\n\\r\\n<p>Your code is run with <code>--harmony</code> flag, enabling <a href=\\\"http://node.green/\\\" target=\\\"_blank\\\">new ES6 features</a>.</p>\\r\\n\\r\\n<p><a href=\\\"https://lodash.com\\\" target=\\\"_blank\\\">lodash.js</a> library is included by default.</p>\\r\\n\\r\\n<p>For Priority Queue / Queue data structures, you may use 5.3.0 version of <a href=\\\"https://github.com/datastructures-js/priority-queue/tree/fb4fdb984834421279aeb081df7af624d17c2a03\\\" target=\\\"_blank\\\">datastructures-js/priority-queue</a> and 4.2.1 version of <a href=\\\"https://githu
