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)

require 'set'

s = gets.strip
k = gets.to_i

# i から始まる substring をすべて上げる
def uniq_substr(s, i, carry, k)
  return carry if s.empty?
  ind = s.index(i)
  return carry if ind.nil?
  len = s.size
  for j in (0..len - ind)
    sub = s[ind..(ind + j)]
    carry << sub
    return carry if carry.size >= k
  end
  uniq_substr(s[(ind+1)..-1], i, carry, k)
end

# puts uniq_substr("abcdabg", "a", Set.new).to_a

count = 0
for i in ('a'..'z')
  sub = uniq_substr(s, i, Set.new, k).to_a.sort
  if count + sub.size >= k
    puts sub[k - count - 1]
    exit 0
  else
    count += sub.size
  end
end