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?

Input

Input is given from Standard Input in the following format:
A B K

Output

Print the answer.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分