Normality concerning the sequence of functions

Let{f_n} be a sequence of functions meromorphic in a domain D, let {h_n} be a sequence of holomorphic functions in D, such that h_n(z)h(z), where h(z)≠ 0 is holomorphic in D, and let k be a positive integer. If for each n ∈ N⁺, f_n(z)≠0 and f_n^(k)(z)-h_n(z) has at most k distinct zeros (ignoring multiplicity) in D, then {f_n} is normal in D.