102481: [AtCoder]ABC248 B - Slimes

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

问题描述

有A个史莱姆。

每次Snuke喊叫，史莱姆就会增加K倍。

为了拥有B个或更多的史莱姆，Snuke至少需要喊叫多少次？

约束条件

• $1 \leq A \leq B \leq 10^9$
• $2 \leq K \leq 10^9$
• 输入中的所有值都是整数。

输入

从标准输入以以下格式获取输入：

$A$ $B$ $K$

输出

打印答案。

样例输入1

1 4 2

样例输出1

2

我们从一个史莱姆开始。 在Snuke的第一声喊叫之后，我们有两个史莱姆；在他的第二声喊叫之后，我们有四个史莱姆。因此，他至少需要喊叫两次才能拥有四个或更多的史莱姆。

样例输入2

7 7 10

样例输出2

0

我们在开始时已经有七个史莱姆。

样例输入3

31 415926 5

样例输出3

6