【原文】A bus with n passengers opens its door at the bus stop. Exactly half of its passengers and an additional half of a passenger get out. On the next stop, again, half of the passengers plus half of a passenger leave the bus. This goes on for k stops in total. Knowing that the bus leaves the last stop empty, and that no one was hurt during the trip, determine the initial number n of people in the bus.

【译文】有一辆载着n人的公交车在到站时打开门，正好有一半的乘客和剩下的一半的乘客下车。下一站也有一半的乘客和剩下的一半的乘客下车（怎么感觉跟绕口令似的）。这种情况总共持续了k站。已知公交车到了最后一站是空的，而且旅途中没人受伤（坐车怎么受伤的）请确定公交车上的初始人数n。