Not sure if facebook will allow that and can block userids you have used considering spammer/hacker.
To be honest, I had an idea that it is not possible unless you know some serious hacking ideas/codes. But looked web for such solutions and found some ideas to do this. Haven't tested yet though.
Please check following answer at stackoverflow which I think is a good point to start with-
c# - Login to the page with HttpWebRequest - Stack Overflow[
^]
This is definitely not the answer but hope it will lead you to get the solution.
Waiting for more people to share their ideas and suggestions.
Thanks
Submit an article or tip