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 <bits/stdc++.h>
using namespace std;
using ll = long long;
using vll = vector<ll>;
#define forn(i,n) for(ll i=0;i<ll(n);++i)
#define all(x) (x).begin(),(x).end()

int main() {
    ios::sync_with_stdio(false);
    string s;
    ll k;
    cin >> s >> k;
    set<string> S;
    ll n = s.size();
    forn(i, n) {
        for (ll j = i; j < n; ++j) {
            string t = s.substr(i, j-i+1);
            if ((ll)S.size() < k || t < *S.rbegin()) {
                S.insert(t);
            }
            else break;
            while ((ll)S.size() > k) {
                S.erase(prev(S.end()));
            }
        }
    }
    cout << *S.rbegin() << '\n';
}