Normal families of meromorphic functions with sharing functions

Let F be a family of meromorphic functions in a domain D, let k be a positive integer, and let h(z)(≡ 0; ∞) be a meromorphic function in D such that any f ∈ F have neither common zeros nor common poles with h(z). If, for each f ∈ F, the multiplicity of the zeros f is at least k, and f = 0 ⇔ f (k) = 0, and f (k) (z) = h(z) ⇒ f(z) = h(z), then F is normal