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: Runtime Error)

#include <bits/stdc++.h>

#define FOR(i,a,b) for(int i=(a);i<(b);i++)
#define rep(i,n) FOR(i,0,n)
#define RFOR(i,a,b) for(int i=(a)-1;i>=(b);i--)
#define rrep(i,n) RFOR(i,n,0)

using namespace std;

typedef long long ll;
typedef unsigned long long ull;

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

	string s;
	cin >> s;

	int k;
	cin >> k;

	int n = s.size();
	vector<string> v;

	FOR(i,1,min(k+1,n)){
		rep(j,n-i+1){
			//cout << i << " " << j << " " << s.substr(j,i) << endl;
			string a = s.substr(j,i);
			auto b = find(v.begin(), v.end(), a);
			if(b == v.end()) v.push_back(s.substr(j,i));	
		}
	}

	// rep(i,v.size()) cout << v[i] << " ";
	// cout << endl;

	sort(v.begin(), v.end());
	cout << v[k-1] << endl;
}