Ann and Half-Palindrome

题面翻译

给定一个只包含 $a,b$ 的字符串 $s(1\le|s|\le5000)$ ，要输出它所有子串中字典序第 $k$ 小的半回文串。若字符串 $t$ 是半回文串 ，则对于 $\forall i\in[1,\frac{|t|+1}{2}]$ 且 $i$ 为奇数，满足 $t_i=t_{|t|-i+1}$ 。数据保证有解。注意同一子串在字典序排列中出现次数与其在 $s$ 中出现次数相同。

题目描述

Tomorrow Ann takes the hardest exam of programming where she should get an excellent mark.

On the last theoretical class the teacher introduced the notion of a half-palindrome.

String $t$ is a half-palindrome, if for all the odd positions $i$ () the following condition is held: $t_{i}=t_{|t|-i+1}$ , where $|t|$ is the length of string $t$ if positions are indexed from $1$ . For example, strings "abaa", "a", "bb", "abbbaa" are half-palindromes and strings "ab", "bba" and "aaabaa" are not.

Ann knows that on the exam she will get string $s$ , consisting only of letters a and b, and number $k$ . To get an excellent mark she has to find the $k$ -th in the lexicographical order string among all substrings of $s$ that are half-palyndromes. Note that each substring in this order is considered as many times as many times it occurs in $s$ .

The teachers guarantees that the given number $k$ doesn't exceed the number of substrings of the given string that are half-palindromes.

Can you cope with this problem?

输入格式

The first line of the input contains string $s$ ( $1<=|s|<=5000$ ), consisting only of characters 'a' and 'b', where $|s|$ is the length of string $s$ .

The second line contains a positive integer $k$ — the lexicographical number of the requested string among all the half-palindrome substrings of the given string $s$ . The strings are numbered starting from one.

It is guaranteed that number $k$ doesn't exceed the number of substrings of the given string that are half-palindromes.

输出格式

Print a substring of the given string that is the $k$ -th in the lexicographical order of all substrings of the given string that are half-palindromes.

样例 #1

样例输入 #1

abbabaab
7

样例输出 #1

abaa

样例 #2

样例输入 #2

aaaaa
10

样例输出 #2

aaa

样例 #3

样例输入 #3

bbaabb
13

样例输出 #3

bbaabb

提示

By definition, string $a=a_{1}a_{2}...\ a_{n}$ is lexicographically less than string $b=b_{1}b_{2}...\ b_{m}$ , if either $a$ is a prefix of $b$ and doesn't coincide with $b$ , or there exists such $i$ , that $ a_{1}=b_{1},a_{2}=b_{2},...\ a_{i-1}=b_{i-1},a_{i}<b_{i} $ .

In the first sample half-palindrome substrings are the following strings — a, a, a, a, aa, aba, abaa, abba, abbabaa, b, b, b, b, baab, bab, bb, bbab, bbabaab (the list is given in the lexicographical order).