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

require 'set'

def read_inputs
  s = gets.chomp
  k = gets.chomp.to_i
  [s, k]
end

s, K = read_inputs
# s = 'atcoderandatcodeer'
# K = 5

chars = s.split ''

class Snippet
  def initialize(s, i, j)
    @s = s
    @i = i
    @j = j
  end
  attr_reader :s, :i, :j

  def hash
    @hash ||= as_ans.hash
  end

  def eql?(other)
    as_ans.eql? other.as_ans
  end

  def to_s
    as_ans + "(#{i},#{j})"
  end

  def inspect
    to_s
  end

  def <=>(other)
    c = 0
    loop do
      out1 = i + c >= j
      out2 = other.i + c >= other.j
      return 0 if out1 && out2
      return -1 if out1
      return 1 if out2
      cand = s[i + c] <=> other.s[other.i + c]
      return cand unless cand.zero?
      c += 1
    end
  end

  def as_ans
    @ans ||= s[i...j]
  end
end

ordered = SortedSet.new
s.size.times do |l|
  (0..(s.size - 1 - l)).each do |i|
    ordered.add(Snippet.new(s, i, i + l + 1))
  end
end

ordered.each.with_index do |e, i|
  if i == K - 1
    puts e.as_ans
    break
  end
end