  We prove that for any discrete curvature satisfying Gauss-Bonnet formula,
there exist a unique up to scaling inversive distance circle packing in the
discrete conformal equivalent class, whose polyhedral metric meets the target
curvature. We prove it by constructing diffeomorphism between fiber bundles
with cell decomposition based on Teichm\"uller spaces, and each discrete
conformal equivalent class is a fiber passing through finite cell with respect
to triangulations, which means we can do surgery on the discrete Ricci flow by
edge flipping using a generalized Ptolemy equation to ensure it converge and
never blow up.
