I think K means it was made in Scotland. Of course I could be wrong, but in the serial numbers for the featherweights I believe its true. There are a few machines that were smaller than the standard so they might have a letter for reference.
If you have a serial number you will find it's birthday here
http://www.singer-featherweight.com/...es/dating.html
Here is an opinion on the 319...
http://sewing-machines.blogspot.com/...forgotten.html