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
$s = trim(fgets(STDIN));
$K = (int)trim(fgets(STDIN));

$ary = [];
for ($i = 0; $i < strlen($s); $i++) {
    for ($j = 1; $j + $i <= strlen($s); $j++) {
        $str = substr($s, $i, $j);
        if (!isset($ary[$str])) {
            $ary[$str] = 1;
        } else {
            $ary[$str]++;
        }
    }
}

ksort($ary);

$i = 1;
foreach($ary as $k => $a) {
    if ($i === $K) {
        echo $k . PHP_EOL;
        exit;
    }
    $i++;
}