mapAccum in monad

I recently had two functions of very similar shape, only difference was that one was pure and the other need some I/O. The former was easily written using mapAccumL. I failed to find a function like mapAccumL that runs in a monad, so I wrote up the following:

mapAccumM :: (Monad m, Traversable t) => (a -> b -> m (a, c)) -> a -> t b -> m (a, t c)
mapAccumM f a l = swap <$> runStateT (mapM go l) a
    where
        go i = do
            s <- get
            (s', r) <- lift $ f s i
            put s'
            return r

Bring on the comments/suggestions/improvements/etc!