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

• $1\le A,B\le 30$
• $1\le K\le S$, 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.

Sample Input 1

2 2 4

Sample Output 1

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.

Sample Input 2

30 30 118264581564861424

Sample Output 2

bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

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