### Problem Statement

You are given three positive integers, X, Y and P. Return the least sum of two positive integers a and b such that P is a divisor of a*X+b*Y.

### Definition

 Class: TheEquation Method: leastSum Parameters: int, int, int Returns: int Method signature: int leastSum(int X, int Y, int P) (be sure your method is public)

### Notes

-The answer is never greater than 2*P: if a = P and b = P, then P is definitely a divisor of a*X+b*Y.

### Constraints

-X, Y and P will each be between 1 and 1000, inclusive.

### Examples

0)

 `2` `6` `5`
`Returns: 3`
 When a=2 and b=1, a*X+b*Y is 10, which is a multiple of P=5. No other valid pair of values for a and b has a smaller sum.
1)

 `5` `5` `5`
`Returns: 2`
 Don't forget that a and b must be positive.
2)

 `998` `999` `1000`
`Returns: 501`
3)

 `1` `1` `1000`
`Returns: 1000`
4)

 `347` `873` `1000`
`Returns: 34`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=6587

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=10791&pm=6587

Vedensky

#### Testers:

PabloGilberto , gawry , lovro , ivan_metelsky

Brute Force