#include <bits/stdc++.h>
using namespace std;
template <class T>
string toStr(const T &x) {
  stringstream s;
  s << x;
  return s.str();
}
template <class T>
int toInt(const T &x) {
  stringstream s;
  s << x;
  int r;
  s >> r;
  return r;
}
int dx[8] = {-1, -1, -1, 0, 1, 1, 1, 0};
int dy[8] = {-1, 0, 1, 1, 1, 0, -1, -1};
bool isPal(string s) {
  for (int i = 0; i <= s.size() / 2; ++i)
    if (s[i] != s[s.size() - i - 1]) return false;
  return true;
}
int main() {
  string s;
  cin >> s;
  int k;
  cin >> k;
  for (int i = 1; i <= s.size(); ++i) {
    int f = true;
    int tot = 0;
    for (int j = 0; j < s.size(); j += i) {
      if (s.size() % i != 0) continue;
      string sub = s.substr(j, i);
      int k = isPal(sub);
      if (!k) f = false;
      tot++;
    }
    if (f and tot == k) {
      cout << "YES";
      return 0;
    }
  }
  cout << "NO";
  return 0;
}

### Prompt

Develop a solution in cpp to the problem described below:

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>
using namespace std;
template <class T>
string toStr(const T &x) {
  stringstream s;
  s << x;
  return s.str();
}
template <class T>
int toInt(const T &x) {
  stringstream s;
  s << x;
  int r;
  s >> r;
  return r;
}
int dx[8] = {-1, -1, -1, 0, 1, 1, 1, 0};
int dy[8] = {-1, 0, 1, 1, 1, 0, -1, -1};
bool isPal(string s) {
  for (int i = 0; i <= s.size() / 2; ++i)
    if (s[i] != s[s.size() - i - 1]) return false;
  return true;
}
int main() {
  string s;
  cin >> s;
  int k;
  cin >> k;
  for (int i = 1; i <= s.size(); ++i) {
    int f = true;
    int tot = 0;
    for (int j = 0; j < s.size(); j += i) {
      if (s.size() % i != 0) continue;
      string sub = s.substr(j, i);
      int k = isPal(sub);
      if (!k) f = false;
      tot++;
    }
    if (f and tot == k) {
      cout << "YES";
      return 0;
    }
  }
  cout << "NO";
  return 0;
}

```