| 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. | |