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.