Codeforces Round #315 (Div. 2) A. Music

A. Music

time limit per test2 seconds
memory limit per test256 megabytes
inputstandard input
outputstandard output

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.

Input

The single line contains three integers T, S, q (2 ≤ q ≤ 104, 1 ≤ S < T ≤ 105).

Output

Print a single integer — the number of times the song will be restarted.

Sample test(s)

input

5 2 2

output

2

input

5 4 7

output

1

input

6 2 3

output

1

题意

下载一首歌，首先加载s秒，然后开始播放和下载，当播放到没下载的点是重新播放，直到听完整首歌，给出歌曲长度T,下载速度q−1q，问开始播放的次数。

题解

就是循环解一个一元一次方程s+q−1qt=t，每次更新s就行(第一发公式写错了，然后最后一分钟被hack。。蠢哭。。。)

AC代码

#include <cstdio>using namespace std;int T,s,q;int ans=1;int main(){    scanf("%d%d%d",&T,&s,&q);    while(q*s<T)        (ans++)&(s*=q);    printf("%d",ans);    return 0;}