Score : $200$ points

问题描述

有 $A$ 个史莱姆。

每次 Snuke 大喊时，史莱姆的数量会乘以 $K$ 倍。

为了拥有 $B$ 或更多的史莱姆，Snuke 至少需要大喊多少次？

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

There are $A$ slimes.

Each time Snuke shouts, the slimes multiply by $K$ times.

In order to have $B$ or more slimes, at least how many times does Snuke need to shout?

Constraints

• $1 \leq A \leq B \leq 10^9$
• $2 \leq K \leq 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$A$ $B$ $K$

Output

Print the answer.

Sample Input 1

1 4 2

Sample Output 1

2

We start with one slime. After Snuke's first shout, we have two slimes; after his second shout, we have four slimes. Thus, he needs to shout at least twice to have four or more slimes.

Sample Input 2

7 7 10

Sample Output 2

0

We have seven slimes already at the start.

Sample Input 3

31 415926 5

Sample Output 3

6

update @ 2024/3/10 10:36:46