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 Python (3.4.3) (judge verdict: Runtime Error)

s = input()
K = int(input())

def count(head):
    cnt = 0
    for i in range(len(s)):
        if i+len(head)-1<len(s) and s[i:i+len(head)]==head:
            cnt += len(s)-i
    return cnt

def solve50(head, K):
    #print('**', head, K)
    W = []
    for i in range(len(s)):
        if i+len(head)-1<len(s) and s[i:i+len(head)]==head:
            for j in range(i, len(s)):
                W.append(s[i:j+1])
                #print(' ', s[i:j+1])
    W = list(set(W))
    W.sort()
    #print(W)
    if len(W)>=K:
        return W[K-1], 0
    else:
        K -= len(W)
        return 0, K

def solve(head, K):
    #print('*', head, K)
    if count(head)<=50:
        return solve50(head, K)
    for a in alphabet:
        if head + a in s:
            #return solve(head + a, K)
            return head + 1, K


alphabet = 'abcdefghijklmnopqrstuvwxyz'

for a in alphabet:
    if not a in s:
        continue

    head = a
    while True:
        ans, K = solve(head, K)
        #print(ans, K)
        if K==0:
            print(ans)
            exit()
        else:
            head = ans

#print('*')