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 5.4.1) (judge verdict: Runtime Error)

#include <stdio.h>
#include <string.h>
#include <stdbool.h>
#include <stdint.h>
#include <stdlib.h>
#include <limits.h>
#include <math.h>
int acs(const void *a, const void *b){return *(int*)a - *(int*)b;} /* 1,2,3,4.. */
int des(const void *a, const void *b){return *(int*)b - *(int*)a;} /* 8,7,6,5.. */
int cmp_char(const void *a, const void *b){return *(char*)a - *(char*)b;} /* a,b,c,d.. */
#define min(a,b) (a < b ? a: b)
#define max(a,b) (a > b ? a: b)
#define rep(i, l, r) for (int i = l; i < r; i++)
#define MAX 51
#define MOD 1000000007

typedef long long int lli;

int cmp_str(const void *a, const void *b){
  return strcmp(*(const char **)a, *(const char **)b);
} /* aaa,aab.. */

int main(void) {
  char s[MAX];
  int k;
  scanf("%s %d", s, &k);

  int cnt = 0;
  char *sub[MAX * 5];
  int n = strlen(s);
  for (int b = 0; b < n; b++) {
    for (int e = b; e < n && e < b + k; e++) {
      int len = e - b + 1;
      sub[cnt++] = strndup(s + b, len);
    }
  }

  qsort(sub, cnt, sizeof(char **), cmp_str);

  int ki = 0;
  for (int ci = 0; ci < cnt; ci++) {
    if ( ki == k ) {
      printf("%s\n", sub[ci - 1]);
      break;
    }
    if ( strcmp(sub[ci], sub[ci + 1]) == 0 ) continue;
    ki++;
  }
  return 0;
}