CPTUI and add_rewrite_endpoint will help you get the desired things.
[Update] From my comment-
You need pairs for rewrite rule /base/1 or base/1/base2/2 using wordpress rewriting… and the way you want will not be that easy depending on wordpress. If you have fixed /custom/continent/country structure then add HTACCESS of your own as site/1/2/3 to yield site/?continent=1&country=2&article=3. This will create global variable in wordpress environment to be queried anytime… 🙂 Hope this helps.