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 (Clang 3.8.0) (judge verdict: Accepted)

#include <stdio.h>
#include <iostream>
#include <string>
#include <vector>
#include <math.h>

using namespace std;

#define AN 26

int to_number(string s){
    int len = s.size();
    int sum = 0;  
    for(int i = 0; i < s.size() && i < 5; i++){
        sum += (s[i] - 'a' + 1) * pow(AN + 1, 4 - i);
    }
    return sum;
}

string _to_string(int n){
    string s = "";
    for(int i = 0; i < 5; i++){
        if(1 <= n % (AN + 1) && n % (AN + 1) <= 26){
            s.push_back(char(n % (AN + 1) + 'a' - 1));
        }
        n = n / (AN + 1);
    }
    reverse(s.begin(), s.end());
    return s;
}

int main(void){
    string s;
    int K;
    cin >> s;
    scanf("%d", &K);

    vector<int> v;
    for(int i = 0; i < s.size(); i++){
        for(int j = 1; j <= 5; j++){
            if(i + j <= s.size())
                //cout << to_number(s.substr(i, j)) << endl;
                v.push_back(to_number(s.substr(i, j)));
        }
    }

    sort(v.begin(), v.end());
    v.erase(unique(v.begin(), v.end()), v.end());

    /*
    for(int i = 0; i < 5; i++){
        cout << _to_string(v[i]) << endl;
    }
    */

    cout << _to_string(v[K - 1]) << endl;


    return 0;
}