Custom Nav Walker menu – Display category count

I have a custom walker menu.( See the code below)

I would like to have my nav menu like this:

Where 495 is the total of the records containing childrens.

Where 42 Number of published articles.

Can someone help me to implement this?
Here is my current custom nav walker code.

<?php
class accordion_Menu_Walker extends Walker_Nav_Menu {
   function start_el(&$output, $item, $depth, $args) {
        global $wp_query;  
        $count_category = '';
     if($item->object == 'publishings')  { 
        $cat_id = $item->object_id;
        $count_category = get_terms('publishings', 'fields=count');
   }           
        $indent = ( $depth ) ? str_repeat( "\t", $depth ) : '';

        $class_names = $value="";
        $classes = empty( $item->classes ) ? array() : (array) $item->classes;
        $classes[] = 'menu-item-' . $item->ID;

        $class_names = join( ' ', apply_filters( 'nav_menu_css_class', array_filter( $classes ), $item, $args ) );
        $class_names=" class="" . esc_attr( $class_names ) . '"';

        $id = apply_filters( 'nav_menu_item_id', 'menu-item-'. $item->ID, $item, $args );
        $id = strlen( $id ) ? ' id="' . esc_attr( $id ) . '"' : '';

        $output .= $indent . '<li' . $id . $value . $class_names .'>';

        $attributes  = ! empty( $item->attr_title ) ? ' title="'  . esc_attr( $item->attr_title ) .'"' : '';
        $attributes .= ! empty( $item->target )     ? ' target="' . esc_attr( $item->target     ) .'"' : '';
        $attributes .= ! empty( $item->xfn )        ? ' rel="'    . esc_attr( $item->xfn        ) .'"' : '';
        $attributes .= ! empty( $item->url )        ? ' href="'   . esc_attr( $item->url        ) .'"' : '';

        $item_output = $args->before;
        $item_output .= '<a'. $attributes .'>';
        $item_output .= $args->link_before . apply_filters( 'the_title', $item->title, $item->ID ) . $args->link_after;
        $item_output .= '(' . $count_category  . ')';
        $item_output .= '</a>';
        $item_output .= $args->after;

        $output .= apply_filters( 'walker_nav_menu_start_el', $item_output, $item, $depth, $args );
    }
}
?>

The code that I use for taxonomy:

add_action( 'init', 'prowp_publishing_taxonomy' );
function prowp_publishing_taxonomy() {
    $labels = array(
        'name'              => 'Категории',
        'singular_name'     => 'Категория',
        'search_items'      => 'Найти Категорию',
        'all_items'         => 'Все категории',
        'parent_item'       => 'Родительская категория',
        'parent_item_colon' => 'Родительские категории:',
        'edit_item'         => 'Редактировать категорию',
        'update_item'       => 'обновить категорию',
        'add_new_item'      => 'Добавить новую категорию',
        'new_item_name'     => 'Новое название категории',
        'menu_name'         => 'Категории'
    );
    $args =array(
        'labels'       => $labels,
        'hierarchical' => true,
        'query_var'    => true,
        'rewrite'      => true
    );
    register_taxonomy( 'type', 'publishings', $args );
}

Help me please do it.

display my current result:

I think you should probably use wp_list_categories(), which even has parameters for a count, like e.g. show_count and pad_counts. Additionally it supports custom walkers via the walker parameter, but the walker would be based on Walker_Category – source -, which gives you every additional styling option you want.