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)

io = STDIN

def substrings(s)
  chars=s.split(//)
  enum=(1..s.size).map do |sz|
    chars.each_cons(sz).to_a.map(&:join)
  end.flatten.uniq
  enum
end

s=io.gets.chomp
k=io.gets.to_i
size=s.size
lc=s.split(//).min
select=(0...size).map do |i|
  j= i+4<size ? i+4 : size-1
  s[i..j]
end.select do |str|
  str[0]==lc
end
select.sort!
ary=(0...([select.size,5].min)).map do |i|
  substrings(select[i])
end.flatten.uniq.sort
puts ary[k-1]