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;
typedef long long ll;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
/*既に塗った色の配列　tuple(親、子、その間の辺の色)の配列
  を用意
*/
struct edge{
    int to,color;
};

using Graph = vector<vector<edge>>;

int main() {
    string S;
    cin >> S;
    int K;
    cin >> K;
    vector<string> vec;
    set<string> s;
    for(int i = 0;i<S.size();i++){
        for(int j = 0;j<S.size()-i;j++){
          s.insert(S.substr(i,j+1));
        }
    }
    for(auto value : s){
        vec.push_back(value);
    }
    sort(vec.begin(),vec.end());
    /*rep(i,vec.size()){
      cout << vec[i] << endl;
    }*/
    cout << vec[K-1] << endl;
  }