All Tracks Math Number Theory Basic Number Theory-2 Problem

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++, C++14, Clojure, C#, D, Erlang, F#, Go, Groovy, Haskell, Java, Java 8, JavaScript(Rhino), JavaScript(Node.js), Julia, Kotlin, Lisp, Lisp (SBCL), Lua, Objective-C, OCaml, Octave, Pascal, Perl, PHP, Python, Python 3, R(RScript), Racket, Ruby, Rust, Scala, Swift, Visual Basic

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Challenge Name

CodeMonk (Number Theory Part I)

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