How can I write a state monad that does error handling as well?

I need to write a state monad that can also support error handling. I was thinking of using the Either monad for this purpose because it can also provide details about what caused the error. I found a definition for a state monad using the Maybe monad however I am unable to modify it to use Either, instead of Maybe. Here's the code:

newtype StateMonad a = StateMonad (State -> Maybe (a, State))

instance Monad StateMonad where
(StateMonad p) >>= k = StateMonad (\s0 -> case p s0 of 
                                 Just (val, s1) -> let (StateMonad q) = k val in q s1
                                 Nothing -> Nothing)
return a = StateMonad (\s -> Just (a,s))

data State = State
{ log  :: String
, a    :: Int}