Split a string into rows using pure SQLite

Using SQLite, I'd like to split a string in the following way.

Input string:

C:\Users\fidel\Desktop\Temp

and have the query return these rows:

C:\
C:\Users\
C:\Users\fidel\
C:\Users\fidel\Desktop\
C:\Users\fidel\Desktop\Temp

In the end I'll probably implement a table-valued function, but before I do, is there a way to do this in pure SQLite?