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: Accepted)

#include <iostream>
#include <string>
#include <vector>
#include <tuple>
#include <algorithm>
#include <cassert>
#define REP(i,k,n) for(int(i)=(k);(i)<(n);++(i))
using namespace std;

string s;
int K;

int main()
{
  cin >> s >> K;
  int N = s.length();           // |s|

  // sの長さKまでの部分文字列
  vector<string> vec;

  REP(j,1,K+1) {
    REP(i,0,N) {

      string t = s.substr(i,j);
      if (t.length() == j) vec.push_back(t);
      else break;               // iからj文字取れなかった

    }
  }

  sort(vec.begin(), vec.end());
  unique(vec.begin(), vec.end());

  assert(vec.size() >= K);
  cout << vec[K - 1] << endl;

  return 0;
}