Matching header data and returning all non-blank values?

Hi all, I have vehicle names in A1:AE1, under each header are actual model years (i.e., 1999, 2001, etc). Some headers only have one year under them, some have eleven. I need a formula (in a separate worksheet) that will match the car name and list each year next to it.

I have the worksheet attached, I'm hoping there is a good array formula that will do this. I think once you open the file, you will understand what I am looking for.

Thank you for your help!!!