Substring Order I

You are given a string of length n. If all of its distinct substrings are ordered lexicographically, what is the kth smallest of them?

Input

The first input line has a string of length n that consists of characters a–z. The second input line has an integer k.

Output

Print the kth smallest distinct substring in lexicographical order.

Constraints

$1 \le n \le 10^5$

$1 \le k \le \frac{n(n+1)}{2}$

$It is guaranteed that k does not exceed the number of distinct substrings.$

Example

Input

babaacbaab
10

Output

aba

Explanation: The 10 smallest distinct substrings in order are a, aa, aab, aac, aacb, aacba, aacbaa, aacbaab, ab, and aba.