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 PHP7 (7.0.15) (judge verdict: Time Limit Exceeded)

<?php
fscanf(STDIN, "%s", $s);
fscanf(STDIN, "%d", $k);

$length = strlen($s);
$memo = [];
for ($i = 0; $i < $length; $i++) {
	for ($len = 1; $len <= $length - $i; $len++) {
		$string = substr($s, $i, $len);
		$count = 0;
		if (array_search($string, $memo, true) !== false) {
			continue;
		}
		foreach ($memo as $key => $str) {
			if ($str !== null && strnatcmp($str, $string) < 0) {
				$count++;
			}
		}
		if ($count < 5) {
			for ($j = 4; $j >= $count; $j--) {
				$memo[$j] = $memo[$j-1];
			}
			$memo[$count] = $string;
		}
	}
}

echo $memo[$k-1], "\n";