P7018 [CERC2013] Bus

# [CERC2013] Bus ## 题面翻译 有一个数 $n$ ，定义一次操作为使 $n\rightarrow \frac{n-1}{2}$ 。已知经过了 $k$ 次操作后 $n$ 恰好为 $0$，求 $n$。 多测，有 $T$ 组数据，$T$ 在输入数据开头给出。 保证 $1\leqslant k\leqslant 30$。 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.

The first line of input contains the number of test cases $T$. The descriptions of the test cases follow: The only line of each test case contains the number of stops $k$, $1 \leq k \leq 30$.

For each test case, output a single line containing a single integer—the initial number of bus passengers. ## 样例 #1 ### 样例输入 #1 ``` 2 1 3 ``` ### 样例输出 #1 ``` 1 7 ```

Time limit: 1000 ms, Memory limit: 1048576 kB. Central Europe Regional Contest (CERC) 2013