CSES - Substring Order II
  • Time limit: 1.00 s
  • Memory limit: 512 MB
You are given a string of length $n$. If all of its substrings (not necessarily distinct) 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 substring in lexicographical order.

Constraints
  • $1 \le n \le 10^5$
  • $1 \le k \le \frac{n(n+1)}{2}$
Example

Input:
baabaa
10


Output:
ab

Explanation: The 10 smallest substrings in order are a, a, a, a, aa, aa, aab, aaba, aabaa, and ab.