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: Time Limit Exceeded)

{-# OPTIONS_GHC -O #-}
{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE ViewPatterns #-}

import Control.Monad
import Data.List
import qualified Data.ByteString.Char8 as B
import qualified Data.Vector as V
import qualified Data.Set as S

sol :: Int -> B.ByteString -> Char -> B.ByteString
sol n s c =
    if sz < n
        then sol (n-sz) s (succ c)
        else S.elemAt (n-1) sets
    where
        sz = S.size sets
        sets = V.foldl' (\set st -> S.insert st set) S.empty ss
        ss = V.concatMap ps $ V.unfoldr fi (0,s)
        fi (o,st) = case B.findIndex (==c) st of
            (Just i) -> Just(o+i, (o+i+1, B.drop (i+1) st))
            Nothing  -> Nothing 
        ps i = V.unfoldr vsnoc $ B.drop i s
        vsnoc bs
            | B.length bs == 0 = Nothing
            | otherwise        = Just (bs, B.init bs)

main = do
    s <- B.getLine
    n <- readLn
    putStrLn $ B.unpack $ sol n s 'a'