Hayman's question on normal families concerning zero numbers

Let m, n and k be three positive integers satisfying nk+m+2, let a(0), b be two finite constants and let F be a family of meromorphic functions in a domain D, all of whose zeros have multiplicity at least k. If, for each function fF, f((k))-af(n)-b has at most m distinct zeros in D, then F is normal in D. Both nk+m+2 and f((k))-af(n)-b have at most m distinct zeros are best possible and all of whose zeros have multiplicity at least k can not be removed.