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Set of subsets without subsubsets
You are given two integers \$n\$ and \$k\$, and are to output a random collection of \$k\$ sets \$\mathcal A_1,\ldots,\mathcal A_k\$ such that:
each \$\mathcal A_i\$ is a subset of \$\{1, 2, \ldots, n\}\$;
no \$\mathcal A_i\$ is a subset of another \$\mathcal A_...