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 <algorithm> // min, max, swap, sort, reverse, lower_bound, upper_bound
#include <bitset>    // bitset
#include <deque>     // deque
#include <iomanip>   //setprecsion
#include <iostream>  // cout, endl, cin
#include <map>       // map
#include <queue>     // queue, priority_queue
#include <set>       // set
#include <stack>     // stack
#include <string>    // string, to_string, stoi
#include <tuple>     // tuple, make_tuple
#include <utility>   // pair, make_pair
#include <vector>    // vector

#include <cctype> // isupper, islower, isdigit, toupper, tolower
#include <cmath>  //sin, cos, tan

using namespace std;
using Graph = vector<vector<int>>;

#define rep(i, n) for (ll i = 0; i < (n); ++i)
#define rrep(i, n) for (ll i = (n - 1); i >= 0; --i)
#define blank(ans) cout << (ans) << " ";
#define mp(p, q) make_pair(p, q)
#define mt(p, q, r) make_tuple(p, q, r)
#define pb(n) push_back(n)
#define all(a) a.begin(), a.end()

typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef string str;

typedef vector<ll> vll;
typedef vector<ld> vd;
typedef vector<bool> vb;
typedef vector<char> vc;
typedef vector<str> vs;
typedef vector<vector<ll>> vvll;
typedef vector<vector<ld>> vvd;
typedef vector<vector<bool>> vvb;
typedef vector<vector<char>> vvc;
typedef vector<vector<str>> vvs;
typedef vector<pair<ll, ll>> vpll;
typedef vector<tuple<ll, ll, ll>> vtlll;

const ld PI = acos(-1.0);
const ll MAX = 9000000000000000000;
const ll MIN = -9000000000000000000;
const ld DMAX = 4500;
const ld DMIN = -4500;
const ll MOD = 1000000007;

template <typename T>
void fin(T a)
{
  cout << a << endl;
  exit(0);
}

void Main()
{
  str s; ll k; cin >> s >> k;
  map <str, ll> flag;
  vs ans;
  for(ll i = 0;i < s.size();i++)
  {
    for(ll j = 1;i + j <= s.size();j++)
    {
      str d = s.substr(i, j);
      if(flag.count(d)) continue;
      else { ans.pb(d); flag[d];}
    }
  }
  sort(all(ans));
  cout << ans[k - 1] << endl;
}

//前処理
int main()
{
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout << fixed << setprecision(20); //高精度少数表示
  //cout << setfill('0') << internal << setw(4); 0埋め４桁
  Main();
  return 0;
}