### Problem Statement

You are developing a new calculator with a square root function. To make things simple for your clients, you have decided to approximate square roots as simple fractions, rather than displaying a long sequence of digits.

You will be given N and D and should return the fraction closest to sqrt(N) for which the denominator is not greater than D. The fraction should be returned in the form "A/B" where A and B are positive integers with no common factors greater than one.

### Definition

 Class: CalcRoot Method: approximate Parameters: int, int Returns: String Method signature: String approximate(int N, int D) (be sure your method is public)

### Constraints

-N will be between 1 and 1000000, inclusive.
-D will be between 1 and 1000, inclusive.

### Examples

0)

 `4` `10`
`Returns: "2/1"`
1)

 `5` `3`
`Returns: "7/3"`
 sqrt(5) = 2.236
2)

 `12` `10`
`Returns: "31/9"`
 sqrt(12) = 3.464
3)

 `23743` `763`
`Returns: "98462/639"`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=4519

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=7221&pm=4519

Andrew_Lazarev

#### Testers:

PabloGilberto , lbackstrom , brett1479

#### Problem categories:

Brute Force, Math