Custom search to display results within same page

I am using the Easy Digital Downloads plugin to sell my music.

I would like to add a custom search form inside the downloads archive page so the results will be displayed on that page.

For example, if you'll go to storename.com/downloads and search for 'whatever', you'll find all the songs that contain 'whatever' in their title.

So, inside the archive-download.php file I added:

div class="search-in-store"

form role="search" method="get" id="searchform" class="searchform" action="?php echo home_url( '/downloads/' ); ?"
div
label class="screen-reader-text" for="find"Search for:/label
input type="text" value="" name="find" id="find" /
input type="hidden" name="post_type" value="download" /
input type="submit" id="searchsubmit" value="Search" /
/div
/form        


?php
if ( isset( $_REQUEST[ 'find' ] ) ) {
// run search query
query_posts( array(
's' = $_REQUEST[ 'find' ],
             'post_type' = $_REQUEST[ 'download' ],
             'paged' = $paged
             )
          );

        // loop
        if ( have_posts() ) : while ( have_posts() ) : the_post();
            // loop through results here
        endwhile; endif;

        // return to original query
        wp_reset_query();
    }
?       

/div

but the problem is that when I'm searching for something, the url changed but the page displays the same content (it didn't filter anything).

https://www.storename.com/downloads/?find=lovepost_type=download

I would like to url above to display ONLY the products with 'love' but it keeps showing all the products.

Any help will be much appreciated. Thank you