200970: [AtCoder]ARC097 C - K-th Substring

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