Problem:
Score : 300 points

Problem Statement

You are given a string s.
Among the different substrings of s, print the K-th lexicographically smallest one.

A substring of s is a string obtained by taking out a non-empty contiguous part in s.
For example, if s = ababc, a, bab and ababc are substrings of s, while ac, z and an empty string are not.
Also, we say that substrings are different when they are different as strings.

Let X = x_{1}x_{2}...x_{n} and Y = y_{1}y_{2}...y_{m} be two distinct strings. X is lexicographically larger than Y if and only if Y is a prefix of X or x_{j} > y_{j} where j is the smallest integer such that x_{j} \neq y_{j}.

Constraints

1 ≤ |s| ≤ 5000

s consists of lowercase English letters.

1 ≤ K ≤ 5

s has at least K different substrings.

Partial Score

200 points will be awarded as a partial score for passing the test set satisfying |s| ≤ 50.

Input

Input is given from Standard Input in the following format:

s
K

Output

Print the K-th lexicographically smallest substring of K.

Sample Input 1

aba
4

Sample Output 1

b

s has five substrings: a, b, ab, ba and aba.
Among them, we should print the fourth smallest one, b.
Note that we do not count a twice.

Sample Input 2

atcoderandatcodeer
5

Sample Output 2

andat

Sample Input 3

z
1

Sample Output 3

z

Solution in C++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;

const int INF = 1e9;

int main() {
  string s;
  cin>>s;
  int k;
  cin>>k;

  int len = s.length();
  for (int c=0; c<26; c++) {
    set<string> substr;
    for (int i=0; i<len; i++) {
      if (s[i] != 'a' + c) continue;
      for (int j=1; j<=len-i; j++) {
        string t = s.substr(i, j);
        substr.insert(t);
      }
    }
    if (substr.size() < k) {
      k -= substr.size();
    } else {
      int cnt = 0;
      for (auto t: substr) {
        ++cnt;
        if (cnt == k) {
          cout<<t<<endl;
          return 0;
        }
      }
    }
  }
}