How do I create a custom Apache log (with just htaccess files) that logs filenames (and paths)?

Question

I have 1and1 shared hosting (for better or worse) and Apache configuration is done via htaccess files - no access to configuration files is provided.

I want to create a custom log to log accesses to files, logging just the filenames, so that I can then, on a daily basis, go through that log and create a sitemap.xml file from it.

What Apache configuration is necessary to do this?