POWTOW - Power Tower City

## 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： $$a^{a^{a^{...}}}$$ （共 $b$ 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 ### 数据范围 $0\le c\le 1000$ $0\le a,b \le 2^{31}-1$

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.

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).

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

3
0 0
2 5
993306745 75707320

1
...719156736
...884765625