[YouTube-API] How to get the thumb of a video for youtube.be url.

Awhile back I found the code below that gets the thumb of a video from a submitted url. The problem is that it works fine for every type of url but the youtube.be shortened version. What do I change to this code to make it grab the thumb of the youtube.be version aswell as the other versions?

   <code>

 function get_youtube_screen_link( $url = '', $type = 'default', $echo = true ) {

    if( empty( $url ) )

        return false;

    if( !isset( $type ) )

        $type = '';

    $url = esc_url( $url );

    preg_match("|[\\?&]v=([^&#]*)|",$url,$vid_id);

    if( !isset( $vid_id[1] ) )

        return false;

    $img_server_num =  'i'. rand(1,4);

    switch( $type ) {

        case 'large':

            $img_link = "http://{$img_server_num}.ytimg.com/vi/{$vid_id[1]}/0.jpg";

            break;

        case 'first':

            // Thumbnail of the first frame

            $img_link = "http://{$img_server_num}.ytimg.com/vi/{$vid_id[1]}/1.jpg";

            break;

        case 'small':

            // Thumbnail of a later frame(i'm not sure how they determine this)

            $img_link = "http://{$img_server_num}.ytimg.com/vi/{$vid_id[1]}/2.jpg";

            break;

        case 'default':

        case '':

        default:

            $img_link = "http://{$img_server_num}.ytimg.com/vi/{$vid_id[1]}/default.jpg";

            break;

    }

    if( $echo )

        echo $img_link;

    else

        return $img_link;

}

</code>

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