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)

def dictionary_sort some_array
  recursive_sort some_array, []
end

def recursive_sort unsorted_array, sorted_array
  return sorted_array if unsorted_array.length == 0
  min = unsorted_array.pop
  tmp = []
  unsorted_array.each do |item|
    if item.upcase < min.upcase
      tmp.push min
      min = item
    else
      tmp.push item
    end
  end
  sorted_array.push min
  recursive_sort tmp, sorted_array
end

substrings=[]
s=gets.chop
k=gets.to_i
n=s.length
for i in 0...n do
  for j in i...n do
    substrings.push(s.slice(i..j))
  end
end

substrings=dictionary_sort(substrings.uniq)
puts substrings.uniq[k-1]