# SP10050 POWTOW - Power Tower City

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• 题目来源
• 评测方式 RemoteJudge
• 标签
• 难度 省选/NOI-
• 时空限制 123ms / 1536MB
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## 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：

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 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： 复制
3
0 0
2 5
993306745 75707320
输出样例#1： 复制

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