I would like to have one login form (either wp-login.php or custom) that will allow my users to sign in into their respective site.

For instance:

www.example.com/site1/ <-- URL to the sub site

Now I want to have the login form at www.example.com where the user can enter site1 and their password and logs in to their sub site, redirect to their dashboard directly.

Is this possible? Thanks folks.