The $day-- doesn't look so good.
It will be much easier and safer to use Time::Local

quoting from there:

use Time::Local 'timelocal_nocheck';

        {
            # The 365th day of 1999
            print scalar localtime timelocal_nocheck 0,0,0,365,0,99;


            # The twenty thousandth day since 1970
            print scalar localtime timelocal_nocheck 0,0,0,20000,0,70;


            # And even the 10,000,000th second since 1999!
            print scalar localtime timelocal_nocheck 10000000,0,0,1,0,
+99;
        }
[download]

Another option is to subtract 60*60*24 from the epoch time and use that.

Cheers.