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/**
* Add log in/out to primary nav  
*/

add_filter( 'wp_nav_menu_items', 'add_loginout_link', 10, 2 );
function add_loginout_link( $items, $args ) {
    if (is_user_logged_in() && $args->theme_location == 'primary') {
        $items .= '<li><a href="'. wp_logout_url() .'">Log Out</a></li>';
    }
    elseif (!is_user_logged_in() && $args->theme_location == 'primary') {
        $items .= '<li><a href="'. site_url('wp-login.php') .'">Log In</a></li>';
    }
    return $items;
}


/**
* Add search bar to specific menu  
*/
add_filter('wp_nav_menu_items','add_search_box_to_menu', 10, 2);
function add_search_box_to_menu( $items, $args ) {
    if( $args->theme_location == 'primary' )
        return $items."<li class='menu-header-search'><form action='http://example.com/' id='searchform' method='get'><input type='text' name='s' id='s' placeholder='Search'></form></li>";

    return $items;
}