Among the strings of length $A + B$ containing $A$ occurrences of a and $B$ occurrences of b, find the string that comes $K$-th in the lexicographical order.

Input is given from Standard Input in the following format:
$A\ B\ K$

Print the answer.

$1≤A,B≤30$
$1 \leq K \leq S$, where $S$ is the number of strings of length $A + B$ containing $A$ occurrences of a and $B$ occurrences of b.
All values in input are integers.

baab

Here are the strings containing two as and two bs in the lexicographical order: aabb, abab, abba, baab, baba, and bbaa. The fourth string, baab, should be printed.