Print to File

I have a Windows 2003 print server that prints hundreds of documents per day to one printer.

Is it possible to set up a "Print to File" where the document would print the file to a directory mapped to another server. I would also need the file name to increment for each file so that it would not overwrite.

For example, I need to send from ServerP to \\ServerA\Share$\ and be named file0001, file0002, file0003, etc...

edited to add: This must be done without user intervention as the printing of the documents is an automatic process.

Thanks!