Using mtl's MonadReader with haskeline has type error

I want use InputT (ReaderT Int IO) a with MonadReader Int.

I write below code to make instance MonadReader on InputT

{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE UndecidableInstances #-}
module HaskelineMonadReader where

import Control.Monad.Reader
import System.Console.Haskeline

instance MonadReader r m => MonadReader r (InputT m) where
    ask = lift ask
    local = mapInputT . local

main :: IO ()
main = putStrLn "HI"

But I get this type error.

HaskelineMonadReader.hs:11:13:
Couldn't match type ‘m0 a0 -> m0 a0’ with ‘forall b. m b -> m b’
Expected type: (m0 a0 -> m0 a0) -> InputT m a -> InputT m a
  Actual type: (forall b. m b -> m b) -> InputT m a -> InputT m a
Relevant bindings include
  local :: (r -> r) -> InputT m a -> InputT m a
    (bound at HaskelineMonadReader.hs:11:5)
In the first argument of ‘(.)’, namely ‘mapInputT’
In the expression: mapInputT . local

How can I fix this error.

Full source code is here

Solution

This compiles:

{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE UndecidableInstances #-}
module HaskelineMonadReader where

import Control.Monad.Reader
import System.Console.Haskeline

instance MonadReader r m => MonadReader r (InputT m) where
    ask = lift ask
    local f = mapInputT (local f)

main :: IO ()
main = putStrLn "HI"

Update

Here is the error message:

Couldn't match type ‘m0 a0 -> m0 a0’
               with ‘forall b. m b -> m b’

Expected type: (m0 a0 -> m0 a0)       -> InputT m a -> InputT m a
Actual type:   (forall b. m b -> m b) -> InputT m a -> InputT m a

So it appears that the expected type is more general because the m0 does not have to be the same as m. In the actual type the m in m b must be the same as the m in m a.