How to refine generic WeakTypeTag inside quasi-quote macro

We have the following typeclass

trait Mapper[A,M[_]]{
  def map[B](a:M[A], f:A => B):M[B]
}

For which we would like to provide instances for specific M. A naive implementation would look like the following:

def materializeMapperImpl[A : c.WeakTypeTag,M[_]](c:blackbox.Context)(implicit mTypeTag:c.WeakTypeTag[M[A]]): c.Expr[Mapper[A,M]] = {
    import c.universe._
    val aType = weakTypeOf[A]
    //println(mTypeTag.toString())
    c.Expr[Mapper[A,M]]{

      q"""
         new Mapper[$aType,$mTypeTag]{
            def map[B](a1:$mTypeTag, f: $aType => B): $mTypeTag = {
              ???
            }
          }
       """
    }
  }

However, this won't compile because the mTypeTag is not refined in its generic arguments and would rather look as List rather than List[Int] and List[String]. How do we refine the mTypeTag, setting its argument to A and B in the macro?