#include <bits/stdc++.h>
using namespace std;
void c_p_c() {}
long long maxSubArraySum(long long a[], long long size) {
  long long max_so_far = INT_MIN, max_ending_here = 0, start = 0, end = 0,
            s = 0;
  for (long long i = 0; i < size; i++) {
    max_ending_here += a[i];
    if (max_so_far < max_ending_here) {
      max_so_far = max_ending_here;
      start = s;
      end = i;
    }
    if (max_ending_here < 0) {
      max_ending_here = 0;
      s = i + 1;
    }
  }
  return 1;
}
long long isPrime(long long n) {
  long long a = 0;
  for (long long i = 2; i * i <= n; i++) {
    if (n % i == 0) return 0;
  }
  return 1;
}
long long bigpower(long long a, long long b) {
  long long res = 1;
  while (b > 0) {
    if (b & 1) {
      res *= a;
    }
    a *= a;
    b >>= 1;
  }
  return res;
}
long long fact(long long n) {
  long long a = 1;
  for (long long i = 1; i <= n; i++) {
    a *= i;
  }
  return a;
}
struct cmp {
  bool operator()(const pair<long long, long long> &a,
                  const pair<long long, long long> &b) const {
    long long la = a.second - a.first + 1;
    long long lb = b.second - b.first + 1;
    if (la == lb) return a.first < b.first;
    return la > lb;
  }
};
long long pal(string s) {
  long long n = s.length();
  long long a = 0;
  for (long long i = 0; i < (n + 1) / 2; i++) {
    if (s[i] != s[n - i - 1]) {
      return 0;
    }
  }
  return 1;
}
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  c_p_c();
  string s;
  cin >> s;
  long long n = s.length();
  long long k;
  cin >> k;
  long long l = n / k;
  if (n % k != 0) {
    cout << "NO" << '\n';
    return 0;
  }
  for (long long i = 0; i < n; i += l) {
    if (!pal(s.substr(i, l))) {
      cout << "NO" << '\n';
      return 0;
    }
  }
  cout << "YES" << '\n';
}

### 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;
void c_p_c() {}
long long maxSubArraySum(long long a[], long long size) {
  long long max_so_far = INT_MIN, max_ending_here = 0, start = 0, end = 0,
            s = 0;
  for (long long i = 0; i < size; i++) {
    max_ending_here += a[i];
    if (max_so_far < max_ending_here) {
      max_so_far = max_ending_here;
      start = s;
      end = i;
    }
    if (max_ending_here < 0) {
      max_ending_here = 0;
      s = i + 1;
    }
  }
  return 1;
}
long long isPrime(long long n) {
  long long a = 0;
  for (long long i = 2; i * i <= n; i++) {
    if (n % i == 0) return 0;
  }
  return 1;
}
long long bigpower(long long a, long long b) {
  long long res = 1;
  while (b > 0) {
    if (b & 1) {
      res *= a;
    }
    a *= a;
    b >>= 1;
  }
  return res;
}
long long fact(long long n) {
  long long a = 1;
  for (long long i = 1; i <= n; i++) {
    a *= i;
  }
  return a;
}
struct cmp {
  bool operator()(const pair<long long, long long> &a,
                  const pair<long long, long long> &b) const {
    long long la = a.second - a.first + 1;
    long long lb = b.second - b.first + 1;
    if (la == lb) return a.first < b.first;
    return la > lb;
  }
};
long long pal(string s) {
  long long n = s.length();
  long long a = 0;
  for (long long i = 0; i < (n + 1) / 2; i++) {
    if (s[i] != s[n - i - 1]) {
      return 0;
    }
  }
  return 1;
}
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  c_p_c();
  string s;
  cin >> s;
  long long n = s.length();
  long long k;
  cin >> k;
  long long l = n / k;
  if (n % k != 0) {
    cout << "NO" << '\n';
    return 0;
  }
  for (long long i = 0; i < n; i += l) {
    if (!pal(s.substr(i, l))) {
      cout << "NO" << '\n';
      return 0;
    }
  }
  cout << "YES" << '\n';
}

```