Are they all palindromes? P21691

You are given a string $s$ and a length $\ell$. Are all the substrings of length $\ell$ of $s$ palindromes?

For instance, let $s =$ “ababa” and $\ell = 3$. Here, we have $s[0..2] =$ “aba”, $s[1..3] =$ “bab” and $s[2..4] =$ “aba”. Since the three substrings of $s$ of length 3 are palindomes, in this case the answer is positive.

Input

Input consists of several cases, each with $s$ and $\ell$. Let $n$ be the size of $s$. You can assume $1 \le \ell \le n \le 10^5$, and that $s$ is made up of only lowercase letters.

Output

For every case, print “yes” or “no”.