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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <cstdio>
#include <iostream>
#include <algorithm>
#include <cstring>
using namespace std;
char s[5005], Str[15];
int arr[5005], chk[10005];
int K;

int Hash(char *str)
{
    long long hap = 37;
    int length;
    length = strlen(str);
    for(int i = 0; i < length; i++)
    {
        hap = (hap * 1234731 + str[i] - 'a') % 10001;
    }
    return hap;
}

bool comp(int t, int u)
{
    if(s[t] == s[u])
    {
        for(int i = 1; i < 5; i++)
        {
            if(s[t + i] == s[u + i])
            {
                continue;
            }
            return s[t + i] < s[u + i];
        }
    }
    return s[t] < s[u];
}

int main()
{
    int length;
    scanf("%s %d", s, &K);
    length = strlen(s);
    s[length] = 100;
    for(int i = 0; i < length; i++)
    {
        arr[i] = i;
    }
    sort(arr, arr + length, comp);
    int count = 0, sidx = 0;
    for(int i = 0; i < length; i++)
    {
        if(count == K)
        {
            printf("%s", Str);
            break;
        }
        if(arr[i] + count < length)
        {
            Str[sidx++] = s[arr[i] + count];
            Str[sidx] = 0;
            if(chk[Hash(Str)] == 1)
            {
                K++;
            }
            chk[Hash(Str)] = 1;
            count++;
            i--;
        }
        else
        {
            K -= count;
            count = 0;
            sidx = 0;
        }
    }
}