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>
void c(char *s,char *t,int l){for(int i=0;i<6;i++)t[i]=i<l?s[i]:0;}
int J(char *s,char *t){for(int i=0;i<6;i++){if(s[i]<t[i])return 1;if(s[i]>t[i])return 0;}return -1;}
int K(char r[7][6],char *t){for(int i=1;i<6;i++)if(J(t,r[i])==-1)return 0;return 1;}
int main(){
  char s[5001],r[7][6],t[6];
  int i,j,k,n,l;
  scanf("%s%d",s,&k);
  for(i=0;i<42;i++)r[i/6][i%6]='}';
  for(n=0;s[n];n++);
  for(i=0;i<n;i++)for(j=1;j<6&&i+j-1<n;j++){
    c(&s[i],t,j);
    if(K(r,t))for(l=5;l>0;l--)if(J(t,r[l])){c(r[l],r[l+1],6);c(t,r[l],6);}
  }
  printf("%s",r[k]);
}