List authors and order by last post date.

I want to list authors with last post title and order them by last post date. Now i have this codes but i don`t know how to edit them.

<?php
//displays all users with their avatar and their posts (titles)
$blogusers = get_users_of_blog();
if ($blogusers) {
foreach ($blogusers as $bloguser) {
$user = get_userdata($bloguser->user_id);
echo '<p>User ID ' . $user->ID . ' ' . $user->user_firstname . ' ' .      $user->user_lastname . '</p>';
  echo get_avatar( $user->ID, 46 );
  $args=array(
  'author' => $user->ID,
  'post_type' => 'post',
  'post_status' => 'publish',
  'posts_per_page' => -1,
  'caller_get_posts'=> 1
);
$my_query = null;
$my_query = new WP_Query($args);
if( $my_query->have_posts() ) {
  //echo 'List of Posts for ' . user->user_firstname . ' ' . $user->user_lastname;
  while ($my_query->have_posts()) : $my_query->the_post(); ?>
    <p><a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to    <?php the_title_attribute(); ?>"><?php the_title(); ?></a></p>
    <?php
  endwhile;
}
  wp_reset_query();  // Restore global post data stomped by the_post().
}
}
?>

I think that alternative way is – list last posts and avoid author duplicating. Please help.