FlatCatsBreeding | Topcoder Archive

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

```
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.
```
4
```
```
3
```
```
4
```
```
Returns: 4
```
After 4 days, the first cat produces 3 kittens, so you will have a total of 4 cats.
```
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.
```
4
```
```
3
```
```
1000000
```
```
Returns: 40
```
```
91
```
```
6
```
```
10433
```
```
Returns: 455
```
```
9
```
```
7
```
```
17079
```
```
Returns: 45
```

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