SOLVE
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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 :
\( 1 \le T \le 10 \)
\( 1 \le A, B ,C \le 10^{12} \)
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 \(25\).