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 <string.h>
#define TRUE 0
#define FALSE 1
#define SIZE 5
#define LEN 6
#define MAX 5000

int Min( int a, int b){
  if( a < b ) return a;
  else        return b;
}

void String_Sort( int size , int len, char data[size][len]){
  /* Using Comb Sort Algorithm */
  int i;
  int h = size;
  int Is_Swapped = FALSE;
  char tmp[LEN];
  
  while( h > 1 || Is_Swapped == TRUE ){
    if( h > 1 ) h = (h * 10) / 13;
    
    for( Is_Swapped = FALSE, i=0; i + h < size; i++){
      if( strcmp(data[i], data[i+h]) > 0 ){
        /* Swap data[i] and data[i+h] */
        strcpy( tmp , data[i] );
        strcpy( data[i] , data[i+h] );
        strcpy( data[i+h] , tmp );
        
        Is_Swapped = TRUE;
      }
    }
  }
}

int main(void){
  int i,n,w,sslen,K;
  char s[MAX];
  char ss[MAX*5][LEN];
  
  scanf("%s",s);
  scanf("%d",&K);
  
  /* Make SubString List */
  for( sslen=0 ,n=1; n<=Min(strlen(s),5); n++){
    for( i=0; i <= strlen(s) - n; sslen++, i++){
      for( w=0; w < n; w++){
        ss[sslen][w] = s[i+w];
        ss[sslen][w+1] = '\0';
      }
    }
  }
  
  String_Sort( sslen, LEN, ss);
  for( i=0, n=sslen, w=0; i < n; i++){
    if( strcmp( ss[i], ss[i+1] ) == TRUE ) sslen--;
    else{
      strcpy( ss[w], ss[i]);
      w++;
    }
  }
  
  printf("%s",ss[K-1]);  
  
  return 0;
}