After making the request, update its offset with the last message.

def _update_offset(self, last_message):
        """
        After making the request, update its offset with the last message.
        """
        self.request.offset_id = last_message.id
        if self.reverse:
            # We want to skip the one we already have
            self.request.offset_id += 1

        if isinstance(self.request, functions.messages.SearchRequest):
            # Unlike getHistory and searchGlobal that use *offset* date,
            # this is *max* date. This means that doing a search in reverse
            # will break it. Since it's not really needed once we're going
            # (only for the first request), it's safe to just clear it off.
            self.request.max_date = None
        else:
            # getHistory and searchGlobal call it offset_date
            self.request.offset_date = last_message.date

        if isinstance(self.request, functions.messages.SearchGlobalRequest):
            self.request.offset_peer = last_message.input_chat