Problem Statement

Find the $K$-th lexicographically smallest string among the strings that are permutations of a string $S$.

What is a permutation of a string?A string $A$ is said to be a permutation of a string $B$ when any character occurs the same number of times in $A$ and $B$.

Constraints

• $1 \\le |S| \\le 8$
• $S$ consists of lowercase English letters.
• There are at least $K$ distinct strings that are permutations of $S$.

Input

Input is given from Standard Input in the following format:

$S$ $K$

Output

Print the answer.

Sample Input 1

aab 2

Sample Output 1

aba

There are three permutations of a string aab: \\{ aab, aba, baa \\}. The $2$-nd lexicographically smallest of them is aba.

Sample Input 2

baba 4

Sample Output 2

baab

Sample Input 3

ydxwacbz 40320

Sample Output 3

zyxwdcba