Problem D
It's a Mod, Mod, Mod, Mod World

You are given multiple problems with three integers $p$, $q$, and $n$. Find $\sum \limits _{i=1}^ n [(p{\cdot }i) \bmod {q}]$. That is, the first $n$ multiples of $p$, modulo $q$, summed. Note that the overall sum has no modulus.


Each input will begin with a line with a single integer $W$ ($1{\le }W{\le }10^5$), which is the number of cases you must solve.

Each of the next $W$ lines will contain three space-separated integers $p$, $q$ and $n$ ($1{\le }p,q,n{\le }10^6$), which are the parameters of the problem as described above.


Output $W$ lines, each with the answer for a given instance of the problem, in the order that they appear in the input.

Sample Input 1 Sample Output 1
2 7 2
1 4 5
3 8 10
CPU Time limit 3 seconds
Memory limit 1024 MB
Source North American Invitational Programming Contest (NAIPC) 2019
License Creative Commons License (cc by-sa)

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