# POWTOW - Power Tower City

## 题意翻译

## 题目描述 给你\$c\$组询问，每组询问给你两个整数\$a,b\$，你需要求： ## \$a^{a^{a^{...}}}(b\$个\$a)\$ 的值。 如\$a=2,b=4\$时，结果为： \$2^{2^{2^2}}=2^{2^4}=2^{16}=65536\$ 特别地，当\$b=0\$时，定义这个式子的值为\$1\$。 如果答案超过\$9\$位数，则先输出“...”，然后输出它的后\$9\$位数。 对于每个询问，单独输出一行。 ## 说明 ### 样例解释 样例有锅，没有显示出来。 样例输出应为： ```cpp 1 ...719156736 ...884765625 ``` ### 数据范围 \$0\le c\le 1000\$ \$0\le a,b \le 2^{31}-1\$

## 题目描述

You are living in a city build entirely of power towers such as 3^3^3 and 10^10^10^10. To enter a building you must type the last 9 digits of the number represented by the tower, written in decimal form, on a keypad next to the main entrance. You are not sharp enough at mental maths, but you can write a handy program to bring along in your pocket. A power tower is defined as repeated exponentiation. We write this using [Knuth's up-arrow notation](http://en.wikipedia.org/wiki/Knuth's_up-arrow_notation) as: e↑↑a = e^e^...^e (a terms). Remember that ^ (exponentiation) is right assosiative. For example: 2↑↑4 = 2^2^2^2 = 2^(2^(2^2)) = 2^2^4 = 2^16 = 65536, and 3↑↑1 = 3. The value of a tower of heigh 0 is 1.

## 输入输出格式

### 输入格式

The first line contains integer C in \[0..1000\], the number of test cases. Then follows C lines, each with integers e,a in \[0..2147483647\]. (non-negative 32-bit ints).

### 输出格式

For each testcase output e↑↑a, or if the output has more than 9 digits, output "..." and then the last 9 digits.

## 输入输出样例

### 输入样例 #1

``````3
0 0
2 5
993306745 75707320``````