Monk and Divisible Numbers
Tag(s):

## Easy-Medium, Modular exponentiation, Prime Factorization, approved

Problem
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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 :

$1 \le T \le 10$

$1 \le A, B ,C \le 10^{12}$

SAMPLE INPUT
2
2 5 2
1029 3861 7652
SAMPLE OUTPUT
25
141813286
Explanation

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 $25$.

Time Limit: 1.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB
Marking Scheme: Marks are awarded when all the testcases pass.
Allowed Languages: C, C++, Clojure, C#, D, Erlang, F#, Go, Groovy, Haskell, Java, Java 8, JavaScript(Rhino), JavaScript(Node.js), Lisp, Lisp (SBCL), Lua, Objective-C, OCaml, Octave, Pascal, Perl, PHP, Python, Python 3, R(RScript), Racket, Ruby, Rust, Scala, Scala 2.11.8, Swift, Visual Basic

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## This Problem was Asked in

Challenge Name

CodeMonk (Number Theory Part I)

OTHER PROBLEMS OF THIS CHALLENGE
• Math > Number Theory
• Math > Number Theory
• Math > Number Theory
• Math > Number Theory