#include <bits/stdc++.h>
using namespace std;
int k;
int n, m;
char str[1001][1001];
char s[1001];
bool ss(char se[]) {
  int len = strlen(se);
  int i;
  for (i = 0; i < len; i++) {
    if (se[i] != se[len - i - 1]) return true;
  }
  return false;
}
int main() {
  int ok, ko, i;
  while (scanf("%s", s) != EOF) {
    ok = 0;
    ko = 0;
    int n;
    scanf("%d", &n);
    int len = strlen(s);
    if (len % n != 0) {
      printf("NO\n");
      continue;
    }
    for (i = 0; i < len; i++) {
      str[ok][ko] = s[i];
      ko += 1;
      if (ko == len / n) {
        ko = 0;
        ok += 1;
      }
    }
    int flag = 0;
    for (i = 0; i < ok; i++) {
      if (ss(str[i])) {
        flag = 1;
        printf("NO\n");
        break;
      }
    }
    if (flag)
      continue;
    else
      printf("YES\n");
    memset(s, '\0', sizeof(s));
    memset(str, '\0', sizeof(str));
    getchar();
  }
  return 0;
}

### Prompt

Your challenge is to write 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;
int k;
int n, m;
char str[1001][1001];
char s[1001];
bool ss(char se[]) {
  int len = strlen(se);
  int i;
  for (i = 0; i < len; i++) {
    if (se[i] != se[len - i - 1]) return true;
  }
  return false;
}
int main() {
  int ok, ko, i;
  while (scanf("%s", s) != EOF) {
    ok = 0;
    ko = 0;
    int n;
    scanf("%d", &n);
    int len = strlen(s);
    if (len % n != 0) {
      printf("NO\n");
      continue;
    }
    for (i = 0; i < len; i++) {
      str[ok][ko] = s[i];
      ko += 1;
      if (ko == len / n) {
        ko = 0;
        ok += 1;
      }
    }
    int flag = 0;
    for (i = 0; i < ok; i++) {
      if (ss(str[i])) {
        flag = 1;
        printf("NO\n");
        break;
      }
    }
    if (flag)
      continue;
    else
      printf("YES\n");
    memset(s, '\0', sizeof(s));
    memset(str, '\0', sizeof(str));
    getchar();
  }
  return 0;
}

```