### Problem Statement

We want to be able to express a fraction as a sum of two fractions that have small denominators. Specifically, given a fraction a/b, we want to find fractions c/d and e/f such that
• a/b = c/d + e/f, where d and f are positive
• max(d,f) is as small as possible
Create a class FracSum that contains a method decompose that is given a and b and that returns the smallest value for max(d,f).

### Definition

 Class: FracSum Method: decompose Parameters: int, int Returns: int Method signature: int decompose(int a, int b) (be sure your method is public)

### Constraints

-a and b will each be between 1 and 2,000,000,000, inclusive.

### Examples

0)

 `14` `10`
`Returns: 5`
 14/10 = 0/1 + 7/5 is one way to keep the denominators less than or equal to 5.
1)

 `1` `60`
`Returns: 12`
 1/60 = -2/5 + 5/12
2)

 `8` `90`
`Returns: 9`
 8/90 = -4/5 + 8/9

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=6520

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=10112&pm=6520

dgoodman

#### Testers:

PabloGilberto , brett1479 , Yarin , Olexiy

Math