Solve the programming task below in a Python markdown code block.
You are given the equation $\tan\alpha=\frac{p}{q}$ and a positive integer, $n$. Calculate $\tan n\alpha$. There are $\mathbf{T}$ test cases.

Input Format

The first line contains $\mathbf{T}$, the number of test cases. 

The next $\mathbf{T}$ lines contain three space separated integers: $p,q$ and $n$, respectively.  

Constraints 

$0\leq p\leq10^9$ 

$1\leq q\leq10^9$ 

$1\leq n\leq10^9$ 

$T\leq10^4$

Output Format

If the result is defined, it is always a rational number. However, it can be very big. 

Output the answer modulo $(10^9+7)$. 

If the answer is $\frac{a}{b}$ and $\boldsymbol{b}$ is not divisible by $(10^9+7)$, there is a unique integer $0\leq x<10^9+7$ where $a\equiv bx\quad\text{mod}\:(10^9+7)$. 

Output this integer, $\boldsymbol{x}$. 

It is guaranteed that $\boldsymbol{b}$ is not divisible by $(10^9+7)$ for all test cases.  

Sample Input
2
2 1 2
5 6 7

Sample Output
666666670
237627959

Explanation

If $\tan\alpha=\frac{2}{1}$ then $\tan2\alpha=-\frac{4}{3}$ and 
$-4\equiv3\times666667670\mod(10^9+7)$. 

So, the answer is $\boldsymbol{66666670}$.