Get method for two variables - php

Question

For some reason the paging does not work with the search get that I have although it was working fine in pages that don't use the get method. If I search for a term lets say example and I have eleven titles in the database that have in their title the word example 10 the first 10 should appear and then in the second page I should have the eleventh one. However when I try to go to the second page the search get from the first page is lost and I get ?pn=$i
<form class="sea" action="search.php" method="GET">
<input class="searchbar" name="search" type="text" placeholder="Search...">
<button class="searchbutton" name="submit-search" type="submit"><i class="fa fa-search"></i></button>
</form>
<?php
if(isset($_GET['submit-search'])) {
$search = mysqli_real_escape_string($conn, $_GET['search']);
$sql = "SELECT COUNT(*) FROM video_games WHERE video_games_title LIKE '%$search%' OR video_games_genre LIKE '$search'";
$query = mysqli_query($conn, $sql);
$row = mysqli_fetch_row($query);
$rows = $row[0];
$page_rows = 10;
$last = ceil($rows/$page_rows);
if($last < 1){
$last = 1;
}
$pagenum = 1;
if(isset($_GET['pn'])){
$pagenum = preg_replace('#[^0-9]#', '', $_GET['pn']);
}
if ($pagenum < 1) {
$pagenum = 1;
}else if ($pagenum > $last) {
$pagenum = $last;
}
$limit = 'LIMIT ' .($pagenum - 1) * $page_rows .',' .$page_rows;
$sql = "SELECT * FROM video_games WHERE video_games_title LIKE '%$search%' OR video_games_genre LIKE '$search' ORDER BY video_games_id $limit ";
$query = mysqli_query($conn, $sql);
$queryResult = mysqli_num_rows($query);
$paginationCtrls = '';
if($last != 1){
if ($pagenum > 1) {
$previous = $pagenum - 1;
$paginationCtrls .= '<i class="fas fa-angle-left"></i> ';
for($i = $pagenum-4; $i < $pagenum; $i++){
if($i > 0){
$paginationCtrls .= ''.$i.' ';
}
}
}
$paginationCtrls .= ''.$pagenum.' ';
for($i = $pagenum+1; $i <= $last; $i++){
$paginationCtrls .= ''.$i.' ';
if($i >= $pagenum+4){
break;
}
}
if ($pagenum != $last) {
$next = $pagenum + 1;
$paginationCtrls .= ' <a href="'.$_SERVER['PHP_SELF'].'?pn='.$next.'"><i class="fas fa-angle-right"></i> ';
}
}
if ($queryResult > 0) {
while($row = mysqli_fetch_array($query, MYSQLI_ASSOC)){
$id = $row["video_games_id"];
$title = $row["video_games_title"];
$genre = $row["video_games_genre"];
$image = $row["video_games_image"];
$description= $row["video_games_description"];
$platform= $row["video_games_platform"];
$price= $row["video_games_price"];
?>
//Putting the data from the database to the html
<?php }//end of while ?>
<div id="pagination_controls"><?php echo $paginationCtrls; ?></div>
If I do some replacements
$paginationCtrls .= ''.$i.' ';
When I press the second page I get the results from the first and the $paginationCtrls also say that I am in the first page eventhough in the url says search=example&submit-search=?pn=2
Why is it not working have I messed with the syntax somwhere?
What can I do to fix it?