POWERUP - Power the Power Up
题意翻译
## 题目描述
给定整数a,b,c,求 $ a^{b^c} mod \;(10^9+7)$
的值
($ 0<=a,b,c<=2^{31}-1$)
备注:$ 0^0=1$
## 输入输出格式
#### 输入格式:
每一行包含3个整数$a,b,c \; (0<=a,b,c<=2^{31}-1)$
当$a=b=c=-1$ 时,输入样例结束
#### 输出格式:
输出每一组a,b,c对应的解,一行一个
## 输入输出样例:
#### 输入样例#1:
````C++
2 2 2
3 4 5
-1 -1 -1
````
#### 输出样例#1:
````C++
16
763327764
````
题目描述
Your younger brother's teacher gave him this simple problem.
Given _b_ and _c_. Evaluate the result of this expression:
_Result_ $ _{1} $ = _b_ $ ^{c} $
Your brother definitely was able to solve this easy problem. So his teacher decided to give him a bit harder problem.
Given _a_,_b_ and _c_. Evaluate the result of this expression:
_Result_ $ _{1} $ = _b_ $ ^{c} $
$ ^{} $ _Result_ $ _{2} $ = _a_ $ ^{Result1} $
However, your brother was also able to solve it. It was not that harder. His teacher was excited -though- and gave him this Bonus Programming Assignment.
Write a program that is given a,b and c; calculates the value of _Result_ $ _{2} $ . Since the output may be exponentially very large, checking the correctness of solutions will be a bit subtle problem. So, instead of printing the whole value of _Result_ $ _{2} $ , just print the reaminder of dividing _Result_ $ _{2} $ by 1,000,000,007 (10 $ ^{9} $ + 7).
Can you help him solve that task?