  In this note we propose an approach for a fast analytic determination of all
possible eigenstates of rational GL(N|M) integrable spin chains of given not
too large length, in terms of Baxter Q-functions. We observe that all
exceptional solutions, if any, are automatically correctly accounted.
  The key intuition behind the approach is that the equations on the
Q-functions are determined solely by the Young diagram, and not by the choice
of the rank of the GL symmetry. Hence we can choose arbitrary N and M that
accommodate the desired representation. Then we consider all distinguished
Q-functions at once, not only those following a certain Kac-Dynkin path.
