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: Runtime Error)

module Ss = Set.Make(String)

let s = read_line ()
let len = String.length s
let k = read_int ()

let f i j set =
  let sub = String.sub s i j in
  if (Ss.mem sub set) then set
  else (Ss.add sub set)

let rec inner i j set =
  if j <= k then
    let set' = f i j set in
    inner i (succ j) set'
  else
    set

let rec outer i set =
  if i <= (len - 1) then
    let set' = inner i 1 set in
    outer (succ i) set'
  else
    set

let () =
  let ls = outer 0 Ss.empty |> Ss.elements in
  let ar = Array.of_list ls in
  let () = Array.fast_sort String.compare ar in
  print_endline ar.(k-1)