IMO 2021 Problem 6

Let $m\ge 2$ be an integer, $A$ a finite set of integers (not necessarily positive) and $B_1,B_2,...,B_m$ subsets of $A$ . Suppose that, for every $k=1,2,...,m$ , the sum of the elements of $B_k$ is $m^k$ . Prove that $A$ contains at least $\dfrac{m}{2}$ elements.