Show first posts with custom field not empty and order all by title

I have a custom post type called "products". My goal is to make my custom query that I have on homepage and also the search query show first the posts that have a custom field called "id_number" not empty and then the other posts that have the "id_number" empty. All should be ordered by title.

This is my code so far only for my custom query. I also need it for search page query but I didn't get that far.

$paged = (get_query_var('paged')) ? get_query_var('paged') : 1;
    $wp_query = new WP_Query( array(
    'post_type' = 'products',
    'posts_per_page' = 20,
    'post_status' = 'publish',
    'pagination' = true,
    'meta_query' = array(
     'relation' = 'OR',
     array( 
           'key' = 'id_number',
           'compare' = 'EXISTS',
                ),
     array( 
          'key' = 'id_number',
           'compare' = 'NOT EXISTS'                
    )
    ),
    'meta_key' = 'id_number',
    'orderby' = 'title',
    'paged'=$paged
    ) ); 

Any help will be appreciated. Thank you!