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?

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.

Note

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).