MaximalProduct | Topcoder Archive

Problem Statement

You are given an integer s and an integer k. Find k positive integers a₁, a₂, ..., a_k such that their sum is equal to s and their product is the maximal possible. Return their product.

Definition

Class:: MaximalProduct
Method:: maximalProduct
Parameters:: int, int
Returns:: long
Method signature:: long maximalProduct(int s, int k)
(be sure your method is public)

Notes

For all valid inputs, the return value will fit in a long.

Constraints

k will be between 1 and 20, inclusive.
s will be between k and 100, inclusive.

Examples

```
10
```
```
3
```
```
Returns: 36
```
The 3 positive integers are 3, 3, 4.
```
10
```
```
1
```
```
Returns: 10
```
```
10
```
```
10
```
```
Returns: 1
```
```
13
```
```
8
```
```
Returns: 32
```
```
7
```
```
2
```
```
Returns: 12
```

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