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: Time Limit Exceeded)

s = gets.chomp
K = gets.to_i
#s = 5000.times.map{('a'..'z').to_a[rand(26)]}.join
#t=Time.now
#K = 5
l = s.length
ss = Array.new(K, nil)
l.times do |i|
    next if ss[K-1] && ss[K-1][0] < s[i]
    #cnt = 0
    (i...l).each do |j|
        str = s[i..j]
        #next if cnt == K - 1
        next if ss.include?(str)
        next if ss[K-1] && ss[K-1] < str
        (0...K).each do |k|
            if !ss[k] || ss[k] > str
                (K-2).downto(k) do |kk|
                    ss[kk+1] = ss[kk]
                end
                ss[k] = str
                #cnt = k
                break
            end
        end
    end
end

puts ss[K-1]
#p Time.now- t