Monday Mutant 113: Blackbarrier Jam (multiplicative)

In this Blackbarrier Jam puzzle, a number indicates the product of two quantities: the number of white cells in an uninterrupted horizontal line from that cell (up to the perimeter or black cells, and including the cell itself), and the number of white cells in an uninterrupted vertical line from that cell (up to the perimeter or black cells, and including the cell itself). The rules are otherwise unchanged.

I'm being commissioned to write puzzles for an iPhone/Windows Phone app; here's a preview of the type of puzzling you can expect to see.