### Problem Statement

An integer x is called a proper divisor of an integer y if x is a divisor of y and 1 <= x < y.

Let us denote as s(a) the sum of all proper divisors of a. An integer a is called almost perfect by k if |a-s(a)| <= k.

You are given ints left, right and k. Return the number of integers between left and right, inclusive, that are almost perfect by k.

### Definition

 Class: AlmostPerfectNumber Method: count Parameters: int, int, int Returns: int Method signature: int count(int left, int right, int k) (be sure your method is public)

### Constraints

-left will be between 2 and 1000, inclusive.
-right will be between left and 1000, inclusive.
-k will be between 0 and 1000, inclusive.

### Examples

0)

 `2` `10` `1`
`Returns: 4`
 The following numbers between 2 and 10 are almost perfect by 1: 2 (s(2) = 1), 4 (s(4) = 3), 6 (s(6) = 6) and 8 (s(8) = 7).
1)

 `5` `5` `5`
`Returns: 1`
2)

 `11` `20` `50`
`Returns: 10`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=7557

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=10881&pm=7557

andrewzta

#### Testers:

PabloGilberto , vorthys , Olexiy , ivan_metelsky

#### Problem categories:

Simple Math, Simple Search, Iteration