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