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: Accepted)

word = gets.chomp.split("")
leng = word.length
nu = gets.to_i
word_s = word.sort
ans = []

if nu == 1
  print word_s[0]
  exit
end
if leng == 2
  ans[0] = word_s[0]
  if word_s[0] == word[0]
    ans[1] = word.join
    ans[2] = word[1]
  else
    ans[1] = word[1]
    ans[2] = word.join
  end
  print ans[nu - 1]
  exit
end

inst = ""
count = 0
count2 = 1
count3 = 1

while count2 < leng
  if word_s[count3] == word_s[count3 - 1]
    word_s.delete_at(count3)
  else
    count3 += 1
  end
  count2 += 1
end


for i in 0..leng - 1
  if word[i] == word_s[0] || word[i] == word_s[1] || word[i] == word_s[2]
    while (count <= 4) && (i + count < leng)
      inst += word[i + count]
      ans.push(inst)
      count += 1
    end
  end
  inst = ""
  count = 0
end

ans_s = ans.sort
leng2 = ans.length
count2 = 1
count3 = 1

while count2 < leng2
  if ans_s[count3] == ans_s[count3 - 1]
    ans_s.delete_at(count3)
  else
    count3 += 1
  end
  count2 += 1
end

print ans_s[nu - 1]