SOLVE
LATER
Given $$3$$ numbers $$A$$, $$B$$ and $$C$$, Monk wants you to tell him the smallest positive integer $$K$$, such that $$ A \times K$$ is evenly divisible by $$B^C$$. In short, you need to tell Monk the smallest $$K$$, such that $$K>0$$, and $$(A \times K) \% (B^C)=0$$.
You shall be given multiple test cases in a single input file. For each test case, print the answer on a new line. As the answer could be rather large, print it Modulo $$10^9+7$$.
Input Format :
The first line contains a single integer $$T$$, denoting the number of test-cases in a single line. Each of the next $$T$$ lines contains $$3$$ space separated integers, i.e. $$A$$, $$B$$ and $$C$$.
Output Format :
For each test case, print the required answer on a new line. As the answer could be rather large, print it Modulo $$10^9+7$$.
Constraints :
$$ 1 \le T \le 10 $$
$$ 1 \le A, B ,C \le 10^{12} $$
For the 1st test in the sample, $$5^2$$=$$25$$. The smallest $$K$$, such that $$A \times K$$ is divisible by $$25$$, is $$25$$.
As $$2 \times 25$$ = $$50$$, that is divisible by $$25$$.