Little Lesha loves listening to music via his smartphone. But the smartphone doesn't have much memory, so Lesha listens to his favorite songs in a well-known social network InTalk.
Unfortunately, internet is not that fast in the city of Ekaterinozavodsk and the song takes a lot of time to download. But Lesha is quite impatient. The song's duration is T seconds. Lesha downloads the first S seconds of the song and plays it. When the playback reaches the point that has not yet been downloaded, Lesha immediately plays the song from the start (the loaded part of the song stays in his phone, and the download is continued from the same place), and it happens until the song is downloaded completely and Lesha listens to it to the end. For q seconds of real time the Internet allows you to download q - 1 seconds of the track.
Tell Lesha, for how many times he will start the song, including the very first start.
The single line contains three integers T, S, q (2 ≤ q ≤ 104, 1 ≤ S < T ≤ 105).
Print a single integer — the number of times the song will be restarted.
5 2 2
2
5 4 7
1
6 2 3
1
In the first test, the song is played twice faster than it is downloaded, which means that during four first seconds Lesha reaches the moment that has not been downloaded, and starts the song again. After another two seconds, the song is downloaded completely, and thus, Lesha starts the song twice.
In the second test, the song is almost downloaded, and Lesha will start it only once.
In the third sample test the download finishes and Lesha finishes listening at the same moment. Note that song isn't restarted in this case.
题目大意：Lesha要听一首长度为T秒的歌。她先下载前S秒，然后开始播放，每当播放到没下载完的地方时，她就从头开始听。下载速度是每q秒下载q-1秒的歌。求Lesha要从头开始几次才能听完（包括第一次开始听）。
设已经下载了S秒，从头开始听x秒后听到没下载完的地方，根据题意可列出方程$\frac{x}{q}=\frac{x-S}{q-1}$，解得$x=S\times q$。所以开始次数就是$\lceil\log_q{\frac{T}{S}}\rceil$。
代码在此。
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