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: Accepted)

module CharMap = Map.Make (Char)

let () =
  let s = read_line () in
  Array.init (String.length s) (fun i -> i, s.[i])
  |> Array.fold_left (fun m (i, c) ->
      CharMap.add c (i :: try CharMap.find c m with Not_found -> []) m) CharMap.empty
  |> CharMap.bindings
  |> List.map (fun (_, is) ->
      List.map (fun i ->
        Array.init 5 (fun n ->
          try [String.init (n + 1) (fun j -> s.[i + j])]
          with _ -> [])
        |> Array.to_list
        |> List.concat) is |> List.concat)
  |> List.concat
  |> List.sort_uniq compare
  |> Scanf.scanf "%d\n" (fun k l -> List.nth l (k - 1))
  |> print_endline