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 Control.Arrow (second)
import Data.List (foldl')
import qualified Data.Set as S
import qualified Data.Vector.Unboxed as V
import qualified Data.ByteString.Char8 as B

solve :: B.ByteString -> Int -> B.ByteString
solve s k = S.toAscList go !! (k-1) where
  go = foldl' go' S.empty [1..k]
  go' arg p = foldl' go'' arg [0..max (B.length s - p) 0] where
    go'' substrs i
      | S.size substrs < k || sub < (S.toAscList substrs) !! (k-1) = S.insert sub substrs
      | otherwise = substrs
      where
        sub = B.take p $ B.drop i s

main = do
  s <- B.getLine
  k <- (fst . (\(Just x) -> x) . B.readInt) <$> B.getLine
  B.putStrLn $ solve s k