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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

# Generated by AtcoderGreedy on 2018-05-12
# ARC097 C
# Your code here

$s = gets.chomp

$K = gets.chomp.to_i - 1

$dict = {}

$s.size.times do |i|
  $dict[$s[i]] ||= []
  $dict[$s[i]] << $s[i]
  (0...i).each do |j|
    $dict[$s[j]] << $s[j..i]
  end
end

$dict = $dict.sort

group = 0

$dict.each do |item|
  key = item[0]
  values = item[1].uniq.sort

  if group <= $K && $K < values.size + group
    puts values[$K - group]
    break
  else
    group += values.size
  end
end