CSES - Substring Order I
  • Time limit: 1.00 s
  • Memory limit: 512 MB
You are given a string of length $n$. If all of its distinct substrings are ordered lexicographically, what is the $k$th 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 $k$th 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.