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>
#define rep(i, n) for (int i = 0; i < n; i++)
using namespace std;
using ll = long long;
using P = pair<int, int>;

string sorted(string s) {
    sort(s.begin(), s.end());
    return s;
}

int main() {
    string s;
    cin >> s;
    int k;
    cin >> k;
    
    int n = s.size();
    set<char> initials;
    rep(i,n) initials.insert(s[i]);
    auto itr = initials.begin();
    set<string> st;
    while(st.size() < k) {
        for (int start = 0; start < s.size(); start++) {
            if (s[start] != *itr) continue;
            int sz = 1;
            while (start + sz <= s.size()) {
                st.insert(s.substr(start, sz));
                sz++;
            }
        }
        itr++;
    }
    auto ans = st.begin();
    rep(i,k-1) ans++;
    cout << *ans << endl;
}