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 {

  def calc(s: String, K: Int): String = {
    val chars = ('a' to 'z').mkString

    def next(str: String): String = {
      val ix = chars.indexOf(str.last)
      if (ix == 25) { // 末尾が'z'
        next(str.dropRight(1))
      } else {
        val c = chars(ix + 1)
        str.dropRight(1) + c
      }
    }

    def step(k: Int, building: String): String = k match {
      case 0 => building.dropRight(1) // 最後に'a'が足されている
      case _ =>
        s.indexOf(building) match {
          case -1 => step(k, next(building))
          case _ => step(k - 1, building + 'a')
        }
    }

    step(K, "a")
  }

  def main(args: Array[String]): Unit = {
    val in = io.Source.fromInputStream(System.in).getLines()
    val s = in.next()
    val K = in.next().toInt
    System.out.println(calc(s, K))
  }
}