Normal family of meromorphic functions concerning limited the numbers of zeros

Let $$k, n \in {\mathbb {N}}, l \in {\mathbb {N}}\backslash \left\{ 1 \right\} , m\in {\mathbb {N}}\cup \left\{ 0 \right\} $$ , and let $$a(z)(\not \equiv 0)$$ be a holomorphic function, all zeros of a(z) have multiplicities at most m. Let $${\mathcal {F}}$$ be a family of meromorphic functions in D. If for each $$f \in {\mathcal {F}}$$ , the zeros of f have multiplicity at least $$k+m$$ , and for $$f\in {\mathcal {F}}$$ , $$f^{l}(f^{(k)})^{n}-a(z)$$ has at most one zero in D, then $${\mathcal {F}}$$ is normal in D.