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 Python (3.4.3) (judge verdict: Runtime Error)

import sys

def makec(c):
  alph = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm',
          'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z']
  if c[-1] == 'z':
    return makec(c[-1])
  else:
    pos = (alph.index(c[-1]) + 1) % 26
    c = c[:-1] + alph[pos]
    return c


def f(S, K, c):
  if K == 0:
    return c[:-1]
  
  if c in S:
    c = c + 'a'
    return f(S, K-1, c)
  else:
    if c > S:
      c = c[:-1]
    c = makec(c)
    return f(S, K, c)

def main():
  input = sys.stdin.readline
  S = str(input().strip())
  K = int(input())
  ans = f(S, K, 'a')
  print(ans)


if __name__ == '__main__':
  main()