Dynamic Parameter List

I'm trying to pull a list of doctors from the Medicare site (http://www.medicare.gov/Physician/Home.asp?bhcp=1), and I'm running into a problem with the parameter list for the scrapeable file.

Once the criteria are entered, the site compiles a list of IDs which it sends to the results page. When I add the results page to my scraping session, I see that there is a separate parameter for each ID. The number of IDs changes depending on the criteria entered.

I can capture the IDs, but I don't know any way to dynamically incorporate them into the parameter list before submitting the scrapeable file. Any ideas?

Thanks.