  We construct a (bi)cyclic sieving phenomenon on the union of dominant maximal
weights for level $\ell$ highest weight modules over an affine Kac-Moody
algebra with exactly one highest weight being taken for each equivalence class,
in a way not depending on types, ranks and levels. In order to do that, we
introduce $\textbf{\textit{S}}$-evaluation on the set of dominant maximal
weights for each highest modules, and generalize Sagan's action by considering
the datum on each affine Kac-Moody algebra. As consequences, we obtain closed
and recursive formulae for cardinality of the number of dominant maximal
weights for every highest weight module and observe level-rank duality on the
cardinalities.
