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 Scala (2.11.7) (judge verdict: Accepted)

object Main extends App {

  def substrList(s: String)(startindex: Int): Seq[String] =
    (startindex + 1 to s.length).take(5).map(l => s.slice(startindex, l))

  val (s, k) = (readLine, readInt)
  val ans = s.zipWithIndex
    .groupBy(_._1)
    .toSeq
    .sortBy(_._1)
    .toStream
    .flatMap {
      case (_: Char, indices: Seq[(Char, Int)]) =>
        indices
          .map(_._2)
          .flatMap(substrList(s))
          .distinct
          .sorted
          .toStream
    }
    .take(k)
    .last

  val ans2 = s.zipWithIndex
    .groupBy(_._1)
    .toSeq
    .sortBy(_._1)
    .toStream
    .flatMap {
      case (_: Char, indices: Seq[(Char, Int)]) =>
        indices
          .map(_._2)
          .flatMap(substrList(s))
          .distinct
          .sorted
          .toStream
    }
    .take(k)
    .last

  println(ans2)
}