hackercupai/hackercup huggingface dataset:
In the not so distant future the world is populated by robots and ruled by an
evil robot emperor. Every robot in the world can be identified by a unique
numeric ID, and the list of all the existing robot IDs is easily accessible to
everyone. One day the emperor decided to call for a general election to
preserve an illusion of democracy. He set it up in the following way:

* \- Every robot can cast at most one vote per round of voting and the votes are anonymous.
* \- The only option on the ballot is the vote for reelection of the emperor.
* \- If at least **P** percent of the population cast votes for the emperor he becomes reelected for the next millennium.
* \- Otherwise the emperor declares the vote void, disassembles **K** robots with the lowest ID numbers (who he finds to be the most rebellious), and then if there are any functional robots left he restarts the whole process.

All the robots are perfectly logical but also rather lazy and prone to
procrastination. That's why after figuring out the plan of the emperor, they
will abstain from voting unless they have to vote to survive the election
(including this round and all later rounds). If they will die whether or not
they vote, they will vote in the hope that the emperor will spare them. (He
won't, because he's evil!).

## Problem

Given **N** \- the initial population size, **K** \- the number of robots
disassembled after an unsuccessful vote and **P** \- the required percentage
of votes.

Compute the number of times the vote will take place.

## Input

The first line contains the number of test cases **T**, where ** 1 ≤ T ≤ 100
**

Each case is a single line with three space-separated integers **N** **K**
**P**

0 < **K** ≤ **N** ≤ 1,000,000,000,000
0 < **P** ≤ 100

## Output

For test case **i**, numbered from **1** to **T**, output "Case #i: ",
followed by a single integer, the number of times the emperor will have to
call a vote before getting reelected.

## Example

In the first case we have three robots. Two of them are facing disassembly, so
they will vote for the emperor. The third robot will survive even if he
abstains in the first round, so he doesn't vote. But two out of three is not
enough to reach the 75% minimum, so the election proceeds to a second round.
The election ends when the single remaining robot casts a vote for the
emperor.

In the second case again two robots are in immediate danger, but the next two
robots are forced to vote as well, otherwise they would end up in the same
situation as in the first example case. Now with the 4 out of 5 casting the
vote the election successfully ends.