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: Wrong Answer)

s = gets.chomp
k = gets.to_i

s.chars.uniq.sort.each do |c|
  pos = 0
  idxs = []
  while pos = s.index(c,pos)
    idxs << pos
    pos += 1
  end
  ss = idxs.map { |i|
    s[i..-1]
  }.sort

  ss_ = Array.new

  (0..ss.length-2).each do |i|
    if ss[i+1].start_with? ss[i]
      # nop
    else
      ss_ << ss[i]
    end
  end

  ss_ << ss[-1]

  ss_.each do |t|
    if k < t.length
      puts t[0..k-1]
      exit 0
    end
    k -= t.length
  end
end