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.chars
k = gets.to_i

str = s[0,k].join
last = nil
s.size.times do |i|
  tmp = s[i, k].join
  if tmp.length < k
    last = s[i, k].join
    break
  end
  str = tmp < str ? tmp : str
end

def create_cands(str)
  cands = []
  chars = str.chars
  while first = chars.shift
    cands << first
    chars.size.times do |i|
      if cands[-1]
        cands << cands[-1] + chars[i]
      else
        cands << chars[i]
      end
    end
  end
  cands.uniq
end

if str.length < k
  if last < str
    if a = create_cands(last)[k-1]
      ans = a
    else
      ans = create_cands(str)[k-1]
    end
  else
    ans = create_cands(str)[k-1]
  end
else
  ans = str
end

puts ans