Yii Nested Set To Dropdown Menu

I’m using Yii nested set behavior, which helps me to keep my categories nested as seen here (nevermind title rows, they are in russian):

And all I want to do is to have Bootstrap nested menu, which should be like this:


    

    $criteria = new CDbCriteria;

    $criteria->order = 'root, lft';

    $categories = Category::model()->findAll($criteria);

    foreach($categories as $i => $category) {

      $items[$i]['label'] = $category->title;

      $items[$i]['url'] = $category->url;

      $items[$i]['active'] = false;

      $items[$i]['items'] = array(

        array('label'=>'123', 'url'=>'#'),

        array('label'=>'123', 'url'=>'#'),

        array('label'=>'123', 'url'=>'#', 'items'=>array(

            array('label'=>'1234', 'url'=>'#'),

            array('label'=>'1234', 'url'=>'#'),

            array('label'=>'1234', 'url'=>'#', 'items'=>array(

                array('label'=>'1234', 'url'=>'#'),

                array('label'=>'1234', 'url'=>'#'),

                array('label'=>'1234', 'url'=>'#'),

            )),

        )),

    ); 

}

$this->widget('bootstrap.widgets.TbMenu', array(

    'type'=>'pills',

    'stacked'=>false, // whether this is a stacked menu

    'items'=>$items

)); 



I don’t understand how to get this done, btw I read this topic and just don’t know how actually apply this function to my problem.

Appreciate any help.