  In this paper, we prove that given a hyperbolic polyhedral metric with an
inversive distance circle packing, and a target discrete curvature satisfying
Gauss-Bonnet formula, there exist a unique inversive distance circle packing
which is discrete conformal to the former one. We deform the surface by
discrete Ricci flow, and do surgery by edge flipping when the orthogonal
circles of some faces are about to be non-compact. The revised weighted
Delaunay inequality of hyperbolic case implies the compactness of the
orthogonal circle. We use a variational principle of a convex Ricci potential
defined on the fiber bundles with cell-decomposition and differential structure
based on Teichm\"uller space to finish the proof.
