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)

{-# LANGUAGE OverloadedStrings, ViewPatterns #-}
import Data.List
import Data.Ord
import Data.Function 
import qualified Data.Set as S
import qualified Data.ByteString.Char8 as B 

main :: IO ()
main = B.getLine >>= main'
    where
        main' s = readLn >>= B.putStrLn . solve s 

-- |
-- >>> B.unpack $ solve (B.pack "aba") 4
-- "b"
-- >>> B.unpack $ solve (B.pack "atcoderandatcodeer") 5
-- "andat"
-- >>> B.unpack $ solve (B.pack "z") 1
-- "z"
solve :: B.ByteString -> Int -> B.ByteString 
solve ss k = dat . head . drop (k - 1) . S.toAscList $ generate S.empty ss
    where
        generate acc xxs@(B.uncons -> Just (_, xs)) = generate acc' xs
            where
                acc' = foldl' (flip S.insert) acc ys
                ys = map wrap . tail . B.inits $ B.take k xxs
        generate acc _ = acc 

newtype S = S { dat :: B.ByteString }
    deriving (Eq)

wrap :: B.ByteString -> S 
wrap = S 

instance Ord S where
    compare = cmp `on` dat

cmp :: B.ByteString -> B.ByteString -> Ordering
cmp (B.uncons -> Just (x, xs)) (B.uncons -> Just (y, ys)) = compare x y `mappend` cmp xs ys
cmp (B.uncons -> Just _) _ = GT
cmp _ (B.uncons -> Just _) = LT
cmp _ _ = EQ