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

For instance, let s = “ababa” and ℓ = 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 ℓ.
Let n be the size of s.
You can assume 1 ≤ ℓ ≤ n ≤ 10^{5},
and that s is made up of only lowercase letters.

Output

For every case, print “yes” or “no”.

Public test cases

**Input**

ababa 3 abracadabra 5 zz 2

**Output**

yes no yes

Information

- Author
- Salvador Roura
- Language
- English
- Official solutions
- C++
- User solutions
- C++