class AsyncScheduler(Scheduler):
    def _update_after_schedule(
        self,
        scheduler_output: SchedulerOutput,
    ) -> None:
        super()._update_after_schedule(scheduler_output)
        for req_id in scheduler_output.num_scheduled_tokens:
            request = self.requests[req_id]
            if (request.num_computed_tokens == request.num_tokens_with_spec +
                    request.num_output_placeholders):
                # The request will generate a new token in this scheduling step.
                request.num_output_placeholders = 1 + self.num_spec_tokens
    def _update_request_with_output(
        self,
        request: Request,
        new_token_ids: list[int],
    ) -> tuple[list[int], bool]:
        status_before_update = request.status
        new_token_ids, stopped = super()._update_request_with_output(
            request, new_token_ids)
        # Cache the new tokens. Preempted requests should be skipped.
        if status_before_update == RequestStatus.RUNNING:
            self.kv_cache_manager.cache_blocks(request, request.num_tokens)
        return new_token_ids, stopped