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 <cmath>
#include <vector>
#include <algorithm>
using namespace std;

const int INF = pow(2, 31) - 1;
#define ll long long
#define DEBUG(x) cout << "DEBUG>" << #x << ":" << x << endl;
#define REP(i,n) for(ll i=0;i<(n);i++)
#define FOR(i,a,b) for(ll i=(a);i<=(b);i++)
ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}

int main() {
  string s;
  cin >> s;
  int K;
  cin >> K;
  vector<string> S;
  REP(i, K) {
    REP(j, s.size() - i) {
      S.push_back(s.substr(j, i + 1));
    }
  }
  sort(S.begin(), S.end());
  S.erase(unique(S.begin(), S.end()), S.end());
  cout << S[K - 1] << endl;
  return 0;
}