adding parent link to submenu

adding parent link to submenu

menu a link to its parent, for example:
I have the following menu:
Parent 1
- Child 1
- Child 2
- Child 3
I wish to add to it (on the fly, not throw the wordpress cms) link to the parent:
Parent 1
- Parent 1
- Child 1
- Child 2
- Child 3
I've searched a lot but got only to this piece of code and I do not know how to continue:
/* Duplicate the parent in a menu */
add_filter( 'wp_nav_menu_objects', 'duplicate_parents' , 10 , 2 );
add_filter( 'wp_nav_menu_items'  , 'duplicate_parents' );

function hasSub($menu_item_id, &$items) {
    foreach ($items as $item)
     {
        if ($item->menu_item_parent && $item->menu_item_parent==$menu_item_id)
        {
            return true;
        }
    }
    return false;
}

$menu_item_parents = array();

function duplicate_parents( $items , $args ) {

 if ( !($args->duplicate_parents) )
   return ($items);


 foreach ($items as $item)
 {
    if ( hasSub($item->ID, &$items) )
    {
       // here I have the parent object, but I do
      //  not know how to add to it data.
    }

 }


 return ($items);  

}