### Problem Statement

A flat cat is a fictional Martian animal known for being an extremely affectionate pet and also for being able to replicate itself promptly given favorable conditions. The cat replicates itself when it is D, 2*D, 3*D, ... days old, and each time, it creates K new kittens. You have been presented with a newborn flat cat. Return the number of days after which you will have at least T cats, assuming that cats don't die.

### Definition

 Class: FlatCatsBreeding Method: days Parameters: int, int, int Returns: int Method signature: int days(int D, int K, int T) (be sure your method is public)

### Constraints

-D will be between 1 and 100, inclusive.
-K will be between 1 and 10, inclusive.
-T will be between 1 and 1000000, inclusive.

### Examples

0)

 `4` `3` `1`
`Returns: 0`
 You have one cat as soon as you are presented with it, so you don't have to wait until it replicates.
1)

 `4` `3` `4`
`Returns: 4`
 After 4 days, the first cat produces 3 kittens, so you will have a total of 4 cats.
2)

 `4` `3` `9`
`Returns: 8`
 After 4 days, you'll have four cats. After 4 more days, each of those cats will produce 3 kittens, for a total of 16 cats. Note that you don't need to have exactly T cats, but at least T.
3)

 `4` `3` `1000000`
`Returns: 40`
4)

 `91` `6` `10433`
`Returns: 455`
5)

 `9` `7` `17079`
`Returns: 45`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=10790

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=14225&pm=10790

Nickolas

#### Testers:

PabloGilberto , ivan_metelsky , StevieT

Brute Force