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 C (GCC 9.2.1) (judge verdict: Accepted)

#include <stdio.h>

char s[5001], t[6];
int sl, tl;
int k, i, iM, j;
char c[6];
inline int strin() {
  i = 0;
  iM = sl - tl;
  while (i <= iM) {
    for (j = 0; j < tl; ++j) {
      if (s[i + j] != t[j]) goto continue_while;
    }
    return 1;
  continue_while:
    ++i;
  }
  return 0;
}
void solve() {
  if (!strin()) return;
  if (k == 0) {
    printf("%s\n", t);
    k = -1;
    return;
  }
  --k;
  ++tl;
  for (c[tl] = 'a'; c[tl] <= 'z'; ++c[tl]) {
    t[tl - 1] = c[tl];
    solve();
    if (k < 0) return;
  }
  --tl;
  t[tl] = 0;
}
int main() {
  scanf("%s", s);
  sl = 5000;
  while (sl - i > 1) {
    j = (sl + i) >> 1;
    if (s[j]) {
      i = j;
    } else {
      sl = j;
    }
  }
  scanf("%d", &k);
  solve();
}