D - aab aba baa

Score : $400$ points

Problem Statement

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.

Constraints

• $1 \leq A, B \leq 30$
• $1 \leq K \leq S$, 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.

Input

Input is given from Standard Input in the following format:

$A$ $B$ $K$

Output

Print the answer.

2 2 4

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.

30 30 118264581564861424

bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

$K$ may not fit into a $32$-bit integer type.