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 <iostream>
#include <assert.h>
#include <algorithm>
#include <string>
#include <list>

void update_list(std::string& substr, std::list<std::string>& list, const int32_t k){
    if(substr == ""){
        return;
    }
    if(list.empty()){
        list.push_back(substr);
        return;
    }
    for(auto it = list.begin(); it != list.end(); it++){
        if(*it == substr){
            return;
        }
        else if(*it > substr){
            list.insert(it, substr);
            if((int32_t)list.size() > k){
                list.pop_back();
            }
            return;
        }
    }
    if((int32_t)list.size() < k){
        list.push_back(substr);
    }
    return;
}

int main(){
    std::cin.tie(0);
    std::ios::sync_with_stdio(false);

    std::string s;
    int32_t K;
    std::cin >> s;
    std::cin >> K;
    std::list<std::string> substr_list;

    for(int32_t i = 0; i < (int32_t)s.size(); i++){
        for(int32_t j = i; j < (int32_t)s.size() && j<i+K; j++){
            std::string substr = s.substr(i,j - i + 1);
            update_list(substr, substr_list, K);
        }
    }

    assert((int32_t)substr_list.size() == K);
    std::cout << substr_list.back() << std::endl;

    return 0;

}