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: Accepted)

#include<stdio.h>
#include<stdlib.h>
#include<math.h>

typedef long long int int64;

#define MAX(a,b) ((a)>(b)?(a):(b))
#define MIN(a,b) ((a)<(b)?(a):(b))
#define ABS(a) ((a)>(0)?(a):-(a))

typedef struct sequence{
  char s[6];
} seq;

int cmp(const void *a,const void *b){
  char *p=((seq *)a)->s;
  char *q=((seq *)b)->s;
  int i=0;
  while(p[i]!='\0' && q[i]!='\0'){
    if(p[i]!=q[i]) return (int)(p[i]-q[i]);
    i++;
  }
  if(p[i]=='\0' && q[i]=='\0') return 0;
  return p[i]=='\0'?-1:1;
}

void run(void){
  char s[5001];
  scanf("%s",s);
  int len=0;
  while(s[len]!='\0') len++;
  int k;
  scanf("%d",&k);
  seq *array=(seq *)malloc(sizeof(seq)*5*len);
  int alen=0;
  int i;
  for(i=1;i<=k;i++){
    int j;
    for(j=0;j+i-1<len;j++){
      int l;
      for(l=0;l<i;l++){
	array[alen].s[l]=s[j+l];
      }
      array[alen].s[l]='\0';
      alen++;
    }
  }
  qsort(array,alen,sizeof(seq),cmp);
  int cnt=0;
  i=0;
  seq t;
  while(cnt<k){
    t=array[i];
    cnt++;
    while(i<alen && cmp(&array[i],&t)==0) i++;
  }
  printf("%s\n",t.s);
  return;
}

int main(void){
  run();
  return 0;
}