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)

def getStr(s, index, length)
  if S.length > index+length 
    s[index..(index+length)]
  end
end

def solve(s, indexs, length, res)
  if indexs.min+length == s.length || length > 5
    return res
  end
  indexs.each{|i|
    res.push(getStr(s, i, length))
  }
  solve(s, indexs, length+1, res)
end

S = gets.chop
K = gets.to_i
min = "a"
result = Array.new()
while result.length < K do
  res = Array.new()
  min_indexs = Array.new()
  offset = 0
  while S.index(min, offset) != nil do
    min_indexs.push(S.index(min, offset))
    offset = min_indexs[-1]+1
  end
  if min_indexs.length > 0 
    res.push(min)
    result.concat(solve(S, min_indexs, 1, res).compact.uniq)
  end
  min = min.succ
end

puts  result.sort[K-1]