Ann and Half-Palindrome

1000ms

524288K

Description:

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 ( $\text{[math]}$ ) 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?

Input:

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.

Output:

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.

Sample Input:

abbabaab
7

Sample Output:

abaa

Sample Input:

aaaaa
10

Sample Output:

aaa

Sample Input:

bbaabb
13

Sample Output:

bbaabb

Note:

By definition, string a = a₁a₂... a_n is lexicographically less than string b = b₁b₂... b_m, if either a is a prefix of b and doesn't coincide with b, or there exists such i, that a₁ = b₁, a₂ = b₂, ... 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).

Informação

Provedor Codeforces

Código CF557E