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<set>
using namespace std;
int main() {
    string s;
    int k;
    cin >> s;
    cin >> k;
    set<string> st;
    for (char c = 'a'; c <= 'z'; ++c) {
        vector<int> v;
        for (int i = 0; i < s.size(); ++i) if (s[i] == c) v.push_back(i);
        for (int j = 1; ; ++j) {
            bool flg = false;
            for (auto itr = v.begin(); itr != v.end(); ++itr) {
                if (*itr + j <= s.size()) st.insert(s.substr(*itr, j)), flg = true;
                else break;
            }
            if (!flg) break;
        }
    }
    for (auto x : st) {
        k--;
        if (k == 0) {
            cout << x << endl;
            break;
        }
    }
    return 0;
}