Estimates of the number of $(k,l)$-sumsets in the finite Abelian group

The subset $A$ of the group $G$ is called $(k,l)$-sumset if there exists subset $B\subseteq G$ such that $A=kB-lB$, where $kB-lB=\{x_1 +\dots +x_k-x_{k+1}\dots - x_{k+l}\mid x_1,\dots, x_{k+l} \in B\}$. Upper and lower bounds of the number of $(k,l)$-sumsets in the Abelian group are obtained.