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 |
---|---|

3 2 7 2 1 4 5 3 8 10 |
6 7 37 |