### Problem Statement

John and Brus are studying string theory at the university. Brus has finished his special project - a dictionary that contains all strings of a special type. Each string in his dictionary contains exactly n occurrences of the lowercase letter 'a', m occurrences of the lowercase letter 'z', and no other letters. The strings are listed in alphabetical order.

Your task is to help John by finding the k-th (1-based) string in Brus's dictionary. If there are less than k strings in the dictionary, return an empty String instead.

### Definition

 Class: TheDictionary Method: find Parameters: int, int, int Returns: String Method signature: String find(int n, int m, int k) (be sure your method is public)

### Constraints

-n will be between 1 and 100, inclusive.
-m will be between 1 and 100, inclusive.
-k will be between 1 and 1,000,000,000 inclusive.

### Examples

0)

 `2` `2` `2`
`Returns: "azaz"`
 There are six strings in the dictionary and the second one is "azaz".
1)

 `2` `2` `6`
`Returns: "zzaa"`
 This string is the last one in the dictionary.
2)

 `10` `10` `1000000000`
`Returns: ""`
 There are less than k strings in the dictionary.
3)

 `7` `4` `47`
`Returns: "aaazazaazaz"`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=10183

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=13519&pm=10183

Vasyl[alphacom]

#### Testers:

PabloGilberto , Olexiy , ivan_metelsky

#### Problem categories:

Dynamic Programming