Fixed Product Minimum Sum - A Proposed New Problem

Clive, thank you!

Problem is ready - by the way now your data generation code creates 3 test-cases - I suppose that's enough?

Dear Clive, thank you for clarification!

As it happens, I feel bewildered. While initially I thought "fractional" version is harder, I solved it first, but with the "integer" one... After several attempts I wrote solution which I don't quite understand - and while it passed once, it seemingly fails on some different input sets. Hopefully I can figure out what is wrong in the morn (and perhaps, why and whether it works at all).