[Haskell-cafe] Accumulating and threading output of functions

Hello all, I have a number of functions, whose type is something like this: f:: a -> b -> (b, c) i.e. it returns a modified b and an additional c. Now I want to write a combinator, which assembles a list of such functions into a single one. This combinator will have to thread the bs from one function to the next and accumulate the cs into a single c. While I was able to write this using a fold, I am not happy with it (my first attempt had a bad error in it, which is always a bad sign). Are you aware of any idioms, how to do such things on the beaten track?