#include <bits/stdc++.h>
bool is_palindrome(std::string::iterator begin, std::string::iterator end) {
  std::string::iterator end_string = end + 1;
  while (begin != end && begin != end_string) {
    if (*begin != *end) {
      return false;
    } else {
      ++begin;
      --end;
    }
  }
  return true;
}
int main() {
  std::string messages;
  int k;
  int split;
  bool palindrome;
  std::cin >> messages;
  std::vector<std::string> strings;
  std::cin >> k;
  std::string::iterator begin = messages.begin();
  std::string new_string;
  split = messages.size() / k;
  palindrome = messages.size() % k == 0 ? true : false;
  while (begin != messages.end() && palindrome) {
    palindrome = is_palindrome(begin, begin + split - 1);
    begin = begin + split;
  }
  std::string answer = palindrome ? "YES" : "NO";
  std::cout << answer << std::endl;
  return 0;
}

### Prompt

Your task is to create a CPP solution to the following problem:

While Mike was walking in the subway, all the stuff in his back-bag dropped on the ground. There were several fax messages among them. He concatenated these strings in some order and now he has string s.

<image>

He is not sure if this is his own back-bag or someone else's. He remembered that there were exactly k messages in his own bag, each was a palindrome string and all those strings had the same length.

He asked you to help him and tell him if he has worn his own back-bag. Check if the given string s is a concatenation of k palindromes of the same length.

Input

The first line of input contains string s containing lowercase English letters (1 ≤ |s| ≤ 1000).

The second line contains integer k (1 ≤ k ≤ 1000).

Output

Print "YES"(without quotes) if he has worn his own back-bag or "NO"(without quotes) otherwise.

Examples

Input

saba
2


Output

NO


Input

saddastavvat
2


Output

YES

Note

Palindrome is a string reading the same forward and backward.

In the second sample, the faxes in his back-bag can be "saddas" and "tavvat".

### Response

```cpp
#include <bits/stdc++.h>
bool is_palindrome(std::string::iterator begin, std::string::iterator end) {
  std::string::iterator end_string = end + 1;
  while (begin != end && begin != end_string) {
    if (*begin != *end) {
      return false;
    } else {
      ++begin;
      --end;
    }
  }
  return true;
}
int main() {
  std::string messages;
  int k;
  int split;
  bool palindrome;
  std::cin >> messages;
  std::vector<std::string> strings;
  std::cin >> k;
  std::string::iterator begin = messages.begin();
  std::string new_string;
  split = messages.size() / k;
  palindrome = messages.size() % k == 0 ? true : false;
  while (begin != messages.end() && palindrome) {
    palindrome = is_palindrome(begin, begin + split - 1);
    begin = begin + split;
  }
  std::string answer = palindrome ? "YES" : "NO";
  std::cout << answer << std::endl;
  return 0;
}

```