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: Runtime Error)

import Control.Monad.ST
import Data.Array.ST

createDjs :: Int -> ST s (STUArray s Int Int)
createDjs n = do newArray (1, n) (-1)

findDjs :: STUArray s Int Int -> Int -> ST s Int
findDjs arr x = do
    x' <- readArray arr x
    if x' < 0
        then
            return x
        else
            do
                x'' <- findDjs arr x'
                writeArray arr x x''
                return x''

mergeDjs :: STUArray s Int Int -> Int -> Int -> ST s ()
mergeDjs arr x y = do
    nx <- readArray arr x
    ny <- readArray arr y
    if nx > ny
        then do
            writeArray arr x y
            writeArray arr y (nx + ny)
        else do
            writeArray arr y x
            writeArray arr x (nx + ny)

addDjs :: STUArray s Int Int -> [Int] -> ST s ()
addDjs arr [x, y] = do
    x' <- findDjs arr x
    y' <- findDjs arr y
    if x' == y'
        then
             return()
        else
            do
                mergeDjs arr x' y'

movable :: STUArray s Int Int -> (Int, Int) -> ST s Int
movable arr (x, y) = do
    x' <- findDjs arr x
    y' <- findDjs arr y
    return $ if x' == y' then 1 else 0

equals :: Int -> [Int] -> [[Int]] -> Int
equals n p edges = runST $ do
    arr <- createDjs n
    mapM_ (addDjs arr) edges
    movable_list <- mapM (movable arr) $ zip [1..] p
    return $ sum movable_list


main :: IO ()
main = do
    [n, m] <- map read . words <$> getLine :: IO [Int]
    p <- map read . words <$> getLine :: IO [Int]
    edges <- mapM (\_->map read . words <$> getLine) [1..m] :: IO [[Int]]
    putStrLn $ show $  equals n p edges