Listing specific file types on directories and subdirectories

Hi friends.
First of all note that I'm not a programmer, i just use php from time to time to solve problems.
So please if what i ask is very easy don't shoot me....

MY GOAL:
I want a script to create a list of specific file type on a directory (and subdirectories) in my server

Let's say that the directory structure on the server is something like this:

../directory/
../directory/SubDir_A1/
../directory/SubDir_A2/
../directory/SubDir_A3/
../directory/SubDir_A3/SubDir_B11/
../directory/SubDir_A3/SubDir_B12/
etc.

I search the web and i find a script:

<?php


//path to directory to scan.
$directory = "./*/";
 
//get all files with a .xxx extension.
$the_files = glob("" . $directory . "*.xxx");
 
$files = '';
// create array
foreach($the_files as $file){ $files[] = "$file"; }


foreach ($files as $value) {
  echo "$value<br>";
}


?>

Code (markup):

I upload the script on ../directory/ (my "main" directory), I run it and i get something like this:

../directory/file1.xxx
../directory/file2.xxx
../directory/file3.xxx
../directory/file4.xxx
etc.

If i change the code to

//path to directory to scan.
$directory = "./*/*/";

Code (markup):

i will get something like this

../directory/SubDir_A1/file11.xxx
../directory/SubDir_A1/file12.xxx
../directory/SubDir_A2/file13.xxx
../directory/SubDir_A3/file14.xxx
etc.

If i change the code to

//path to directory to scan.
$directory = "./*/*/*/";

Code (markup):

i will get something like this

../directory/SubDir_A3/SubDir_B11/file11.xxx
../directory/SubDir_A3/SubDir_B11/file12.xxx
../directory/SubDir_A3/SubDir_B12/file13.xxx
../directory/SubDir_A3/SubDir_B12/file14.xxx
etc.

WHAT I'M LOOKING FOR....

Is there a way to modify the script and after uploading the script to my main directory (../directory/) and run it to get this type of list:

../directory/file1.xxx
../directory/file2.xxx
../directory/file3.xxx
../directory/file4.xxx
../directory/SubDir_A1/file11.xxx
../directory/SubDir_A1/file12.xxx
../directory/SubDir_A2/file13.xxx
../directory/SubDir_A3/file14.xxx
../directory/SubDir_A3/SubDir_B11/file11.xxx
../directory/SubDir_A3/SubDir_B11/file12.xxx
../directory/SubDir_A3/SubDir_B12/file13.xxx
../directory/SubDir_A3/SubDir_B12/file14.xxx
etc.

Please Advise
Thank you.