#include <bits/stdc++.h>
#pragma comment(linker, "/stack:227420978")
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
using namespace std;
const long long MOD = 1000000007LL, INF = 1e9, LINF = 1e18;
const long double PI = 3.141592653589793116, EPS = 1e-9,
                  GOLD = ((1 + sqrt(5)) / 2);
long long keymod[] = {1000000007LL, 1000000009LL, 1000000021LL, 1000000033LL};
vector<long long> HashMod(keymod, keymod + sizeof(keymod) / sizeof(long long));
template <class T>
int getbit(T s, int i) {
  return (s >> i) & 1;
}
template <class T>
T onbit(T s, int i) {
  return s | (T(1) << i);
}
template <class T>
T offbit(T s, int i) {
  return s & (~(T(1) << i));
}
template <class T>
int cntbit(T s) {
  return __builtin_popcount(s);
}
auto TimeStart = chrono::steady_clock::now();
auto TimeEnd = chrono::steady_clock::now();
long long n, k;
string s;
void ControlIO(int argc, char* argv[]);
void TimerStart();
void TimerStop();
void Exit();
bool isPalin(string st) {
  string za = st;
  reverse(za.begin(), za.end());
  return (za == st);
}
void Input() {
  cin >> s >> k;
  n = s.size();
}
void Solve() {
  if (n % k > 0) {
    cout << "NO";
    return;
  }
  for (long long i = 0; i < n; i += n / k) {
    string st = s.substr(i, n / k);
    if (!isPalin(st)) {
      cout << "NO";
      return;
    }
  }
  cout << "YES";
}
int main(int argc, char* argv[]) {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  ControlIO(argc, argv);
  Input();
  TimerStart();
  Solve();
  TimerStop();
  return 0;
}
void ControlIO(int argc, char* argv[]) {}
void TimerStart() {}
void TimerStop() {}
void Exit() {
  TimerStop();
  exit(0);
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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>
#pragma comment(linker, "/stack:227420978")
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
using namespace std;
const long long MOD = 1000000007LL, INF = 1e9, LINF = 1e18;
const long double PI = 3.141592653589793116, EPS = 1e-9,
                  GOLD = ((1 + sqrt(5)) / 2);
long long keymod[] = {1000000007LL, 1000000009LL, 1000000021LL, 1000000033LL};
vector<long long> HashMod(keymod, keymod + sizeof(keymod) / sizeof(long long));
template <class T>
int getbit(T s, int i) {
  return (s >> i) & 1;
}
template <class T>
T onbit(T s, int i) {
  return s | (T(1) << i);
}
template <class T>
T offbit(T s, int i) {
  return s & (~(T(1) << i));
}
template <class T>
int cntbit(T s) {
  return __builtin_popcount(s);
}
auto TimeStart = chrono::steady_clock::now();
auto TimeEnd = chrono::steady_clock::now();
long long n, k;
string s;
void ControlIO(int argc, char* argv[]);
void TimerStart();
void TimerStop();
void Exit();
bool isPalin(string st) {
  string za = st;
  reverse(za.begin(), za.end());
  return (za == st);
}
void Input() {
  cin >> s >> k;
  n = s.size();
}
void Solve() {
  if (n % k > 0) {
    cout << "NO";
    return;
  }
  for (long long i = 0; i < n; i += n / k) {
    string st = s.substr(i, n / k);
    if (!isPalin(st)) {
      cout << "NO";
      return;
    }
  }
  cout << "YES";
}
int main(int argc, char* argv[]) {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  ControlIO(argc, argv);
  Input();
  TimerStart();
  Solve();
  TimerStop();
  return 0;
}
void ControlIO(int argc, char* argv[]) {}
void TimerStart() {}
void TimerStop() {}
void Exit() {
  TimerStop();
  exit(0);
}

```