All reviewers support accept. One point that was discussed after the rebuttal period was the following: The work  by Mourtada and Gaïffas proves the same result when C=0 or more generally for the "adversarial with a gap" setting, so how much more work is needed to show the general case with C\neq 0 considered in this paper? Given only two very brief mentions of  in the paper, this is highly unclear to the readers. Note that in [32, 33], this generalization is almost trivial. While reviewers do not believe that this is also the case here, we do agree that much more discussions on this are needed. So please make this clearer in the final version, along with other minor issues pointed out in the reviews.