Using Horizontal Layout with Fit To Parent

I want to have a Horizontal Layout Group that behaves as follows:

The first item fills the height of the Horizontal Layout Group, and matches it's width to it's height, so that it's always square.

Then, then second item fills the rest of the remaining space in the Horizontal Layout Group, stretching to fit the remaining height and width

Ideally, I could create a third square item that could even go on the opposite end.

I have attached a doodle to help

Thanks