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.

Input

Input is given from Standard Input in the following format:
S K

Output

Print the answer.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分