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>
 
int main(){
	char s[5001];
	scanf("%s",s);
	int K;
	scanf("%d",&K);
	
	int l=strlen(s);
	int c=0;
	for(int i=0;i<K;i++)c+=l-i;
	
	char sub[c][K+1];
	
	int cc=0;
	for(int i=1;i<=K;i++){
		for(int j=0;j<l-i+1;j++)
{
			for(int k=0;k<i;k++)
{
				sub[cc][k]=s[j+k];
				if(k==i-1)for(k;k<K;k++)sub[cc][k+1]='\0';
			}
			cc++;
		}
	}
	
	//sort
	int r=c;
	int swapped=0;
	while(r>1 || swapped==1)
{
		if(r>1)r=r*10/13;
		swapped=0;
		for(int i=0;i+r<c;i++)
{
			if(strcmp(sub[i],sub[i+r])>0)
{
				char tmp[K+1];
				for(int j=0;j<K+1;j++)tmp[j]=sub[i][j];
				for(int j=0;j<K+1;j++)sub[i][j]=sub[i+r][j];
				for(int j=0;j<K+1;j++)sub[i+r][j]=tmp[j];
				swapped=1;
			}
		}
	}
	
	int k=1;
	for(int i=0;i<c;i++)
{
		if(i>0 && strcmp(sub[i-1],sub[i])!=0)k++;
		if(k==K)
{
			printf("%s\n",sub[i]);
			return 0;
		}
	}
	
	//for(int i=0;i<c;i++)printf("%s\n",sub[i]);
	
	return 0;
}