如何修复在wordpress帖子中显示为空的显示日期

I am editing code in template tags to show the last modified date on my WordPress website, what I mean is if I update the post, it should conditionally show update and ignore "Published", and if I do not, it should leave as is.

I got it to work, the problem I have is "Published On" appearing on all my post: http://prntscr.com/nn9hfl, this is my code so far

    function chicken_wings_posted_on() {

            /**
            * Function to show last updated date
            */

                $u_time = get_the_time('U'); 
                $u_modified_time = get_the_modified_time('U'); 
                if ($u_modified_time >= $u_time + 86400) { 
                echo '<p class = "last-updated-up">Last updated on '; 
                the_modified_time('F jS, Y'); 
                echo "</p> "; } 

                else { 
                echo '<p class = "entry-date published">Published on '; 
                the_time('F jS, Y'); 
                echo "</p> "; }



        $time_string = sprintf( $time_string,
            esc_attr( get_the_date( 'c' ) ),
            esc_html( get_the_date() ),
            esc_attr( get_the_modified_date( 'c' ) ),
            esc_html( get_the_modified_date() )
        ); 

        $posted_on = sprintf(
            /* translators: %s: post date. */
            esc_html_x( 'Published on %s', 'post date', 'chicken-wings' ),
            '<a href="' . esc_url( get_permalink() ) . '" rel="bookmark">' . $time_string . '</a>'
        );

I expect the result to be showing Updated Date only if a post is updated only

I can spot the problem is between the $posted_on = sprintf(, and I can see that is including permalink on the actual date, how do I correct the code to include the permalink in the updated date if post updated, and the actual date if not updated.

Thanks.