How do I configure rsyslog to write to /var/log/{hostname of sender} when receiving remote logs?

My ADSL modem supports remote logging via syslog. I have set up my server, running rsyslog, to accept the log messages from the modem and they are being show in /var/log/syslog along with the messages generated on the server. The log looks like this:

(timestamp) (hostname) (program): (message)

Where hostname is either server or modem.

I’ve look over the (terrible, IMO) documentation, and found this example that looks like what I need, but I can’t make it work in my situation.

How do I configure rsyslog to write the logs received from the modem to /var/log/modem instead of /var/log/syslog?

The modem IP is static, if that helps to simplify the answer.

Moderators: This post should probably have a rsyslog tag instead of syslog, but my reputation isn’t high enough to create it.

$template DynaFile,"/var/log/%HOSTNAME%"
*.* -?DynaFile