E. Ann and Half-Palindrometime limit per test1.5 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputTomorrow 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: ti = 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?InputThe 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.OutputPrint 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.ExamplesInputabbabaab7OutputabaaInputaaaaa10OutputaaaInputbbaabb13OutputbbaabbNoteBy definition, string a = a1a2... an is lexicographically less than string b = b1b2... bm, if either a is a prefix of b and doesn't coincide with b, or there exists such i, that a1 = b1, a2 = b2, ... ai - 1 = bi - 1, ai < bi.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). 
Inputabbabaab7
Outputabaa
['data structures', 'dp', 'graphs', 'string suffix structures', 'strings', 'trees', '*2300']