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: Wrong Answer)

#include <iostream>
#include <string>
#include <cstdlib>
#include <climits>
#include <cmath>
#include <vector>
#include <algorithm>
#include <utility>
 
using namespace std;
 
#define FOR(var,start,end) for(int var=start; var<end; var++)
#define REP(var,cnt) FOR(var,0,cnt)

int DP[5010][26];
 
int main(void) {
	
	string str;
	cin >> str;
	int K;
	cin >> K;
	
	int N = str.size();
	if ( N > 100 ) { return 0; }
	
	vector<string> vec;
	REP(i, N) {
		for(int j=1; j<=(N-i); j++) {
			vec.push_back( str.substr(i, j) );
		}
	}
	sort(vec.begin(), vec.end());
	vec.erase(unique(vec.begin(), vec.end()), vec.end());
	
	cout << vec[K-1] << endl;
	/*
	int i = 0;
	string ret;
	while(true) {
		REP(j, 26) {
			if ( K > DP[i][j] ) {
				K -= DP[i][j];
			} else if ( K <= DP[i][j] ) {
				
			} else {
				
			}
	}
	*/
}