#include <bits/stdc++.h>
using namespace std;
long long rdtsc() {
  long long tmp;
  asm("rdtsc" : "=A"(tmp));
  return tmp;
}
inline int myrand() { return abs((rand() << 15) ^ rand()); }
inline int rnd(int x) { return myrand() % x; }
const int INF = (int)1e9 + 1;
const long double EPS = 1e-9;
void precalc() {}
int n, k;
const int maxn = (int)1e3 + 10;
char s[maxn];
bool read() {
  if (scanf("%s%d", s, &k) < 2) {
    return 0;
  }
  return 1;
}
void solve() {
  n = (int)strlen(s);
  bool fail = 0;
  if (n % k) {
    fail = 1;
  } else {
    int len = n / k;
    for (int i = 0; !fail && i < n; i += len) {
      for (int j = 0; j < len / 2; ++j) {
        if (s[i + j] != s[i + len - 1 - j]) {
          fail = 1;
          break;
        }
      }
    }
  }
  printf(fail ? "NO\n" : "YES\n");
}
int main() {
  srand(rdtsc());
  precalc();
  while (1) {
    if (!read()) {
      break;
    }
    solve();
  }
  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;
long long rdtsc() {
  long long tmp;
  asm("rdtsc" : "=A"(tmp));
  return tmp;
}
inline int myrand() { return abs((rand() << 15) ^ rand()); }
inline int rnd(int x) { return myrand() % x; }
const int INF = (int)1e9 + 1;
const long double EPS = 1e-9;
void precalc() {}
int n, k;
const int maxn = (int)1e3 + 10;
char s[maxn];
bool read() {
  if (scanf("%s%d", s, &k) < 2) {
    return 0;
  }
  return 1;
}
void solve() {
  n = (int)strlen(s);
  bool fail = 0;
  if (n % k) {
    fail = 1;
  } else {
    int len = n / k;
    for (int i = 0; !fail && i < n; i += len) {
      for (int j = 0; j < len / 2; ++j) {
        if (s[i + j] != s[i + len - 1 - j]) {
          fail = 1;
          break;
        }
      }
    }
  }
  printf(fail ? "NO\n" : "YES\n");
}
int main() {
  srand(rdtsc());
  precalc();
  while (1) {
    if (!read()) {
      break;
    }
    solve();
  }
  return 0;
}

```