| 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. |
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|
| 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 |
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|
| Given **N** \- the initial population size, **K** \- the number of robots |
| disassembled after an unsuccessful vote and **P** \- the required percentage |
| of votes. |
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|
| Compute the number of times the vote will take place. |
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|
| ## 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** |
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|
| 0 < **K** ≤ **N** ≤ 1,000,000,000,000 |
| 0 < **P** ≤ 100 |
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|
| ## Output |
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| 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. |
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|
| 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. |
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|
