OCaml function with data type tree

We are give a tree that contains two types of elements. It is defined with the following data-structure.

type ( 'a , 'b ) tree =   Empty   | Vertexa of 'a * ( 'a , 'b ) tree list   | Vertexb of 'b * ( 'a , 'b ) tree list

Write a function split: ('a,'b) tree ->'a list * 'b list, that saves all elements of type 'a to the first list and all elements of type 'b in the second list.

I had an idea of doing this recursively but I am kind of stuck on this. I will attach my attempt even though it does not work at all :/

let rec one drevo_list=    match drevo_list with   | [Empty]->Empty    | Empty::tl -> one tl   | Vertexa(a,b)::tl -> Vertexa(a,b@tl)    | Vertexb(a,b)::tl -> Vertexb(a,b@tl) 

This function turns a list into a tree. I needed it for the recursion, since the second parametar in Vertexa or Vertexb is a list. And this worksBut the recursion part does not.

let rec split drevo=   match drevo with   | Empty -> [],[]   | Vertexa(a,b)-> split (one b)   | Vertexb(a,b)-> split (one b)

This part does not work and I have no idea how to finish it. Does any one have an idea how to finish this?