vk011 on "Pagination not working with custom wp_query"

I am trying to make a custom search plugin but pagination does not work (it shows up with the correct number pages but does not function properly).

Relevant part of the search plugin (from the main function.

$blog_url = get_bloginfo('url');

    $form = <<<EOH
    <div id="sbc">
    <form method="get" action="{$blog_url}" id="ss-search">
        <input type="text" value="{$search_text}" name="supers" onblur="if (this.value == '') { this.value = '{$search_text}';}" onfocus=if (this.value == '{$search_text}') { this.value = '';}" />
        {$list}
        <input type="submit" id="sbc-submit" value="Search" />
    </form>
    </div>
EOH;

///////////////////////////////////

    if (isset($_GET['supers'])) {

        global $q;
        // global $q;
        $args = array(
            // 'category__not_in' => 1,
            's' => $_GET['supers']
        );

        $q = new WP_Query($args);

        if ( $q->have_posts() ) {
                echo '<ul>';
            while ( $q->have_posts() ) {
                $q->the_post();
                echo '<li>' . get_the_title() . '</li>';
            }
                echo '</ul>';
                // echo '<br>Posts found :'.$q->found_posts.'<br><br>';
                echo get_pagination_links2();
        } else {
            echo 'no posts found';

        }

        /* Restore original Post Data */
        wp_reset_postdata();
    }

    return $form;

} // end function
$q; // add ability to make it global

pagination function in the functions.php file

function get_pagination_links2() {
    global $q;
    // echo gettype($q);
    echo $q->found_posts;
    $big = 999999999;

    return paginate_links( array(
        'base' => str_replace( $big, '%#%', esc_url( get_pagenum_link( $big ) ) ),
        'format' => '?paged=%#%',
        'current' => max( 1, get_query_var('paged') ),
        'total' => $q->max_num_pages,
        'prev_next'    => true
    ) );

}

I DO get pagination links, but they don't work (for example if I click next the URL changes but the results don't).