#include <bits/stdc++.h>
using namespace std;
inline int Set(int N, int pos) { return N = N | (1 << pos); }
inline int Reset(int N, int pos) { return N = N & ~(1 << pos); }
inline bool check(int N, int pos) { return (bool)(N & (1 << pos)); }
template <class T>
T gcd(T a, T b) {
  return (a % b == 0) ? b : gcd(b, a % b);
}
template <class T>
T lcm(T a, T b) {
  return (a / gcd(a, b)) * b;
}
template <class T>
bool is_prime(T n) {
  if ((n % 2 == 0 && n > 2) || n < 2) return 0;
  for (T i = 3; i * i <= n; i = i + 2) {
    if (n % i == 0) return 0;
  }
  return 1;
}
string s;
bool val(int i, int j) {
  for (; i <= j; i++, j--) {
    if (s[i] != s[j]) return 0;
  }
  return 1;
}
int main() {
  int k;
  cin >> s >> k;
  if (s.size() % k) {
    cout << "NO\n";
  } else {
    int l = s.size() / k;
    for (int i = 0; i < s.size(); i += l) {
      if (!val(i, i + l - 1)) {
        cout << "NO\n";
        return 0;
      }
    }
    cout << "YES\n";
  }
  return 0;
}

### Prompt

Please create a solution in Cpp 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>
using namespace std;
inline int Set(int N, int pos) { return N = N | (1 << pos); }
inline int Reset(int N, int pos) { return N = N & ~(1 << pos); }
inline bool check(int N, int pos) { return (bool)(N & (1 << pos)); }
template <class T>
T gcd(T a, T b) {
  return (a % b == 0) ? b : gcd(b, a % b);
}
template <class T>
T lcm(T a, T b) {
  return (a / gcd(a, b)) * b;
}
template <class T>
bool is_prime(T n) {
  if ((n % 2 == 0 && n > 2) || n < 2) return 0;
  for (T i = 3; i * i <= n; i = i + 2) {
    if (n % i == 0) return 0;
  }
  return 1;
}
string s;
bool val(int i, int j) {
  for (; i <= j; i++, j--) {
    if (s[i] != s[j]) return 0;
  }
  return 1;
}
int main() {
  int k;
  cin >> s >> k;
  if (s.size() % k) {
    cout << "NO\n";
  } else {
    int l = s.size() / k;
    for (int i = 0; i < s.size(); i += l) {
      if (!val(i, i + l - 1)) {
        cout << "NO\n";
        return 0;
      }
    }
    cout << "YES\n";
  }
  return 0;
}

```