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: Wrong Answer)

import Data.List

-- 部分文字列をまともに求めると爆発するのでn文字で足きり
-- n+1文字の文字列から先頭から1,..,n文字までの部分文字列が辞書順で前に来る
substrings :: Int -> String -> [String]
substrings _ "" = []
substrings 0 _ = []
substrings n s@(_:r) = (substrings' n s) ++ (substrings (n - 1) r)
    where
        substrings' _ "" = []
        substrings' 0 _ = []
        substrings' n (c:r) = [c:""] ++ (map ((:)c) $ substrings' (n - 1) r)

pickup_small :: Ord a => Int -> [a] -> [a]
pickup_small n l = take' n $ sort $ nub l
    where
        take' n l = take (minimum [n, length l]) l

kth :: Int -> String -> String
kth k s = (foldr f [] $ substrings k s) !! (k - 1)
    where
        f e r = pickup_small k (e:r)

main = do
    s <- getLine
    k <- readLn
    putStrLn $ kth k s