Widget : Default Recent Posts – change order

I’d like to modify the default Recent Posts widget so the post titles are displayed in ascending sequence.

I found the function WP_Widget_Recent_Posts in the default-widgets.php file and I inserted the following code:

<?php query_posts($query_string . '&orderby=date&order=ASC'); ?>

Immediately before the loop code:

<?php while ($r->have_posts()) : $r->the_post(); ?>

Unfortunately (even though it looks like the_post is reset in the function, the order of the widget remained in DESC sequence. But the order of the main post loop changed to ASC which is not what I want.

Any ideas what I need to do to just change the order in the default widget?