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? 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. 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. 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 ,