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 <iostream>
#include <vector>
#include <map>
#include <algorithm>
#define rep(i, n) for(int i = 0; i<n; i++)

using namespace std;

int main(void) {
    string s;
    int k;
    cin >> s >> k;
    k--;

    vector<string> subs;
    map<string, bool> memo;

    rep(start, s.size()) {
        string si = s.substr(start, 1);
        if(subs.size()==k+1 and si > subs[k]) continue;
        rep(li, s.size()-start) {
            int l = li+1;
            string si = s.substr(start, l);
            auto it = lower_bound(subs.begin(), subs.end(), si);
            if (memo.count(si)) continue;
            // cout << si << endl;

            subs.insert(it, si);
            if (subs.size() > k) subs.resize(k+1);
            memo[si] = true;
        }
    }
    cout << subs[k] << endl; 
}