How to access Choice Field Value by using Lookup Field in REST API?

I have a list(ListA) which has a lookup field(LookupF) for another list(ListB). ListB includes a choice field(ChoiceF) which can take a single value.

I want to call the selected value of the ChoiceF by using the LookupF in SP 2013 REST API.

This url doesn't work:

http://appWebUrl/_api/web/lists/getByTitle("ListA")/items?$select=LookupF/ChoiceF&$expand=LookupF

Error:The query to field 'LookupF/ChoiceF'isnot valid.

On the other if I create a calculated field(CalculatedF) which is equal to the value of ChoiceF ([=ChoiceF]) in ListB, then I can access the value using the following url:

http://appWebUrl/_api/web/lists/getByTitle("ListA")/items?$select=LookupF/CalculatedF&$expand=LookupF

I do not want to create unnecessary fields like these, just to be able to get the selected choice values. Is there any direct way to access choice values for lookup fields?