Negative contact surgery on Legendrian non-simple knots

We prove that for any pair of Legendrian representatives of the Chekanov-Eliashberg twist knots with different LOSS invariants, any negative rational contact r-surgery with r≠ -1 always gives rise to different contact 3-manifolds distinguished by their contact invariants. This gives the first examples of pairs ofLegendrian knots with the same classical invariants but distinct contact r-surgeries for all negative rational number r. We also generalize the statement from the twist knots to a certain families of two bridge knots.