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 <algorithm>
#include <iostream>
#include <iomanip>
#include <cstring>
#include <string>
#include <vector>
#include <random>
#include <bitset>
#include <queue>
#include <cmath>
#include <stack>
#include <set>
#include <map>
#define rep(i,n) for (int i=0; i<n;++i)
using namespace std;
string s, ans;
int K;

int search(vector<int> &T, int r){
    vector<string> C;
    int a = s.size();
    rep(i, T.size()){
        for(int j=1; j<=min(r, a - T[i]); j++){
            C.push_back(s.substr(T[i], j));
        }
    }
    sort(C.begin(), C.end());
    C.erase(unique(C.begin(), C.end()), C.end());
    if(C.size() < r) return r - C.size();
    
    ans = C[r-1];
    return 0;
}

int main() {
    cin.sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);

    cin >> s >> K;
    vector<pair<char, int> > S(s.size());
    rep(i, s.size()){
        S[i].first = s[i];
        S[i].second = i;
    }

    sort(S.begin(), S.end());
    if(K==1){
        cout << S[0].first << endl;
        return 0;
    }
    int t = 0;
    while(t < S.size()){
        vector<int> T;
        char trgt = S[t].first;
        T.push_back(S[t].second);
        t++;
        while((t < S.size()) & (trgt == S[t].first)){
            T.push_back(S[t].second);
            t++;
        }
        K = search(T, K);
        if(K == 0) break;
    }

    cout << ans << endl;
    return 0;
}