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 (4.10.0) (judge verdict: Time Limit Exceeded)

Scanf.scanf "%s %d" (fun s k ->
    let module S = Set.Make (struct type t = string let compare = compare end) in

    let n = String.length s in

    let rec loop st en set =
        if st = n then set else
            if en = n then loop (st + 1) (st + 1) set else
                loop st (en + 1) (S.add (String.sub s st (en - st + 1)) set)
    in
    let set = loop 0 0 S.empty in

    let rec loop i set =
        let m = S.min_elt set in
        if i = k then m else loop (i + 1) (S.remove m set)
    in
    loop 1 set |> print_endline
)