  Let $D$ be a proper domain in the extended complex plane ${\mathbb
C}_{\infty}:={\mathbb C}\cup \{\infty\}$, $M=M_+-M_-\not\equiv \pm \infty$ be a
difference of non-trivial subharmonic functions $M_{\pm}\not\equiv \mp \infty$
on $D$, $\text{Hol}(D,M)$ be the class of holomorphic function $f$ on $D$
satisfying $|f|\leq \text{const}_f\exp M$ om $D$, ${\sf Z}\subset D$ be a
sequence of points in $D$ without limits points in $D$. We give a complete
description of the conditions under which the sequence $\sf Z$ is a sequence of
all zeros for some nonzero function $f\in \text{Hol}(D,M)$.
