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 qualified Data.Vector.Unboxed as V
import Data.Array.IArray (listArray, accumArray, (!))
import Data.Array.MArray
import Data.Array.ST (STUArray, runSTUArray)
import Data.Array.Unboxed (UArray)
import Data.List (sortOn, sortBy, unfoldr, partition)
import Data.Char (isSpace)
import qualified Data.Set as S
import Control.Monad.ST (ST)
import Control.Monad.Trans.State (StateT(..))
import qualified Data.ByteString.Char8 as B

-- utility functions

--   Input functions
readInt = B.readInt . B.dropWhile isSpace

readInts :: Int -> B.ByteString -> [Int]
readInts n = take n . unfoldr readInt

readIntsV :: Int -> B.ByteString -> V.Vector Int
readIntsV n = V.unfoldrN n readInt

readIntsA :: Int -> B.ByteString -> UArray Int Int
readIntsA n bs = runSTUArray $ do
  arr <- newArray_ (0,n-1)
  go arr 0 bs
  return arr
  where
    go :: STUArray s Int Int -> Int -> B.ByteString -> ST s ()
    go arr i bs
      | i==n = return ()
      | otherwise = do
        let Just (x,bs') = readInt bs
        writeArray arr i x
        go arr (i+1) bs'

readTsV :: Int -> B.ByteString -> V.Vector (Int,Int)
readTsV n = V.unfoldrN n $ runStateT ((,) <$> StateT readInt <*> StateT readInt)

readTs :: Int -> B.ByteString -> [(Int,Int)]
readTs n = take n . unfoldr readT where
  readT = runStateT ((,) <$> StateT readInt <*> StateT readInt)

-- main

enumKSubStrings :: Int -> B.ByteString -> S.Set B.ByteString
enumKSubStrings k bs = S.unions $ map (enum . B.take k) (B.tails bs) where
  enum bs = foldr S.insert S.empty (tail $ B.inits bs)

main = do
  bs <- B.getLine
  k <- read <$> getLine
  B.putStrLn . (!!(k-1)) . S.toList . enumKSubStrings k $ bs