  We show how to extend the Karolyi-Nagy beautiful proof of the
Zeilberger-Bressoud q-Dyson theorem, (first proved by Zeilberger and Bressoud
in 1985, and originally conjectured by George Andrews in 1975), that states
that the constant term of a certain Laurent polynomial equals the q-multinomial
coefficient, how to evaluate any other specific coefficient. The algorithm
implies that any such coefficient is always a certain rational function (that
the algorithm finds) times the q-multinomial coefficient.
