Advanced Evaluate Curve

This is an issue that comes up repetitively in all my projects. I've searched the forum here each time and never found a solution. I think I even remember someone posting it wasn't possible. I do think it is though, I just can't figure out how. Thank you for your help.

- I know the length of the complete black line.

- I want to control the length of the blue and red lines with sliders.

- I want GH to divide the black line so that the resulting pieces grow expontentially from the red to the blue length, yielding the grey pieces below.

- It is important that for all grey pieces, their length is smaller than that of blue, and larger than that of red.

- The count of grey pieces is not important, as long as their lengths conform the requirements. Of course it would be extra nice if the count could be controlled as well, as I believe the requirements can be met for more than one count.

Ideally I could control the "expontentialness" of the transition at hand of a slider too, rather than a graph mapper (although this is usually easy as you can use the ReMap component for t's to enter).

So far I have experimented with custom remapping of several domains that I was hoping could describe the intervals. No success though.