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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Data.List

substrings s = concat [substrings' s i | i<-[1..(min 5 (length s))]]
  where
    substrings' s@(x:xs) i
      | length s == i = [s]
      | otherwise = (take i s) : (substrings' xs i)

main = do
  s <- getLine
  k <- readLn :: IO Int

  putStrLn $ (solve [] (substrings s)) !! (k-1)
  
  where
    solve :: [String] -> [String] -> [String]
    solve sorted [] = sorted
    solve sorted (x:xs) = solve s xs
      where s = sort' sorted x

    sort' sorted x
      | elem x sorted = sorted
      | length sorted < 5 = sort $ x:sorted
      | last sorted <= x = sorted
      | otherwise = init (sort $ x:sorted)