CN-TST 2011 Problem 8

Let $\ell$ be a positive integer, and let $m,n$ be positive integers with $m\geq n$ , such that $A_1,A_2,\cdots,A_m,B_1,\cdots,B_m$ are $m+n$ pairwise distinct subsets of the set $\{1,2,\cdots,\ell\}$ . It is known that $A_i\Delta B_j$ are pairwise distinct, $1\leq i\leq m, 1\leq j\leq n$ , and runs over all nonempty subsets of $\{1,2,\cdots,\ell\}$ . Find all possible values of $m,n$ .