#include <bits/stdc++.h>
double const EPS = 3e-8;
using namespace std;
template <class T>
T gcd(T a, T b) {
  return (b != 0 ? gcd<T>(b, a % b) : a);
}
template <class T>
T lcm(T a, T b) {
  return (a / gcd<T>(a, b) * b);
}
template <class T>
inline bool read(T &x) {
  int c = getchar();
  int sgn = 1;
  while (~c && c < '0' || c > '9') {
    if (c == '-') sgn = -1;
    c = getchar();
  }
  for (x = 0; ~c && '0' <= c && c <= '9'; c = getchar()) x = x * 10 + c - '0';
  x *= sgn;
  return ~c;
}
string inp;
bool isOk(int x, int y) {
  while (x < y) {
    if (inp[x] != inp[y]) return 0;
    x++;
    y--;
  }
  return 1;
}
int main() {
  cin >> inp;
  int a = ({
    int a;
    read(a);
    a;
  });
  int sz = inp.size();
  if (sz % a) {
    puts("NO");
    return 0;
  }
  int lim = sz / a;
  int s = 0, i;
  for (i = s; i < sz; i += lim) {
    if (isOk(i, i + lim - 1) == 0) {
      puts("NO");
      return 0;
    }
  }
  puts("YES");
  return 0;
}

### Prompt

Your task is to create 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>
double const EPS = 3e-8;
using namespace std;
template <class T>
T gcd(T a, T b) {
  return (b != 0 ? gcd<T>(b, a % b) : a);
}
template <class T>
T lcm(T a, T b) {
  return (a / gcd<T>(a, b) * b);
}
template <class T>
inline bool read(T &x) {
  int c = getchar();
  int sgn = 1;
  while (~c && c < '0' || c > '9') {
    if (c == '-') sgn = -1;
    c = getchar();
  }
  for (x = 0; ~c && '0' <= c && c <= '9'; c = getchar()) x = x * 10 + c - '0';
  x *= sgn;
  return ~c;
}
string inp;
bool isOk(int x, int y) {
  while (x < y) {
    if (inp[x] != inp[y]) return 0;
    x++;
    y--;
  }
  return 1;
}
int main() {
  cin >> inp;
  int a = ({
    int a;
    read(a);
    a;
  });
  int sz = inp.size();
  if (sz % a) {
    puts("NO");
    return 0;
  }
  int lim = sz / a;
  int s = 0, i;
  for (i = s; i < sz; i += lim) {
    if (isOk(i, i + lim - 1) == 0) {
      puts("NO");
      return 0;
    }
  }
  puts("YES");
  return 0;
}

```