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 OCaml (4.02.3) (judge verdict: Time Limit Exceeded)

let () =
  let s = Scanf.scanf "%s " (fun a -> a) in
  let k = Scanf.scanf "%d " (fun a -> a) in

  let srd l = 
    let sl = List.sort compare l in
    let rec go l acc = match l with
      | [] -> List.rev acc
      | [x] -> List.rev (x::acc) 
      | (x1::x2::xs) -> 
        if x1 = x2
        then go (x2::xs) acc
        else go (x2::xs) (x1::acc)
    in go sl []
  in

  let length = String.length s in

  let rec f str fst fnl res = 
    if fst = length then res else (
      let res = (String.sub str fst fnl) :: res in
      if (fst + fnl = length || fnl - fst = k) then
        f str (fst+1) 1 res
      else
        f str fst (fnl+1) res
    )

  in
  let lst = f s 0 1 [] in
  let lst = srd lst in

  print_endline (List.nth lst (k-1))