OIM 2021 Problem 5

For a finite set $C$ of integer numbers, we define $S(C)$ as the sum of the elements of $C$ . Find two non-empty sets $A$ and $B$ whose intersection is empty, whose union is the set $\{1,2,\ldots, 2021\}$ and such that the product $S(A)S(B)$ is a perfect square.