  The hybrid NLIE of AdS_5 x S^5 is applied to a wider class of states. We find
that the Konishi state of the orbifold AdS_5 x (S^5/Z_S) satisfies A_1 NLIE
with the source terms which are derived from contour deformation trick. For
general states, we construct a deformed contour with which the contour
deformation trick yields the correct source terms.
