#include <bits/stdc++.h>
using namespace std;
string s;
int judge(string a) {
  int l = a.length() / 2;
  for (int i = 0; i < l; i++)
    if (a[i] != a[a.length() - 1 - i]) return 0;
  return 1;
}
int k;
int main() {
  cin >> s;
  scanf("%d", &k);
  int len = s.length(), cnt = 0, flag = 0;
  if (len % k == 0) {
    int l = len / k;
    for (int i = 0; i < k; i++)
      if (judge(s.substr(i * l, l))) cnt++;
    if (cnt == k) flag = 1;
  }
  if (flag)
    puts("YES");
  else
    puts("NO");
}

### Prompt

Please formulate 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>
using namespace std;
string s;
int judge(string a) {
  int l = a.length() / 2;
  for (int i = 0; i < l; i++)
    if (a[i] != a[a.length() - 1 - i]) return 0;
  return 1;
}
int k;
int main() {
  cin >> s;
  scanf("%d", &k);
  int len = s.length(), cnt = 0, flag = 0;
  if (len % k == 0) {
    int l = len / k;
    for (int i = 0; i < k; i++)
      if (judge(s.substr(i * l, l))) cnt++;
    if (cnt == k) flag = 1;
  }
  if (flag)
    puts("YES");
  else
    puts("NO");
}

```