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: Accepted)

from sys import stdin
from string import ascii_lowercase


def myfind(s, c):
    result = []
    for i, x in enumerate(s):
        if x == c:
            result.append(i)
    return result


def main():
    s = stdin.readline().rstrip()
    K = int(stdin.readline().rstrip())
    result = []
    for x in ascii_lowercase:
        idxs = myfind(s, x)
        if not idxs:
            continue
        result.append(x)
        if len(result) >= K:
            break
        temp = sorted(list(set([s[x:] for x in idxs])))
        for y in temp:
            for z in range(len(y)):
                foo = y[: z + 1]
                if not foo in result:
                    result.append(foo)
                    if len(result) >= K:
                        break
            if len(result) >= K:
                break
        if len(result) >= K:
            break

    print(result[-1])


if __name__ == '__main__':
    main()