#include <bits/stdc++.h>
using namespace std;
template <class T>
class compare {
 public:
  bool operator()(pair<T, T> &x, pair<T, T> &y) {
    if (x.first == y.first) {
      return x.second > y.second;
    }
    return x.first > y.first;
  }
};
template <class T>
ostream &operator<<(ostream &os, const pair<T, T> &a) {
  os << a.first << " " << a.second;
}
template <class T>
void print(vector<T> &vec) {
  for (int i = 1; i < (int)vec.size(); i++) cout << vec[i] << " ";
  cout << endl;
}
template <class T>
void print(set<T> &s) {
  for (auto it : s) cout << it << " ";
  cout << endl;
}
template <class T>
void print(list<T> &lst) {
  for (auto it : lst) cout << it << " ";
  cout << endl;
}
template <class T>
long long power(T a, int b) {
  long long po = 1;
  while (b--) po *= a;
  return po;
}
template <class T>
pair<T, T> operator+(const pair<T, T> &a, const pair<T, T> &b) {
  return {a.first + b.first, a.second + b.second};
}
template <class T>
pair<T, T> operator-(const pair<T, T> &a, const pair<T, T> &b) {
  return {a.first - b.first, a.second - b.second};
}
template <class T>
pair<T, T> operator*(const pair<T, T> &a, const pair<T, T> &b) {
  return {a.first * b.first, a.second * b.second};
}
template <class T>
pair<T, T> operator%(const pair<T, T> &a, const pair<T, T> &b) {
  return {a.first % b.first, a.second % b.second};
}
template <class T, class U>
pair<T, T> operator+(const pair<T, T> &a, const U &b) {
  return {a.first + b, a.second + b};
}
template <class T, class U>
pair<T, T> operator*(const pair<T, T> &a, const U &b) {
  return {a.first * b, a.second * b};
}
int Set(int N, int pos) { return N = N | (1 << pos); }
int reset(int N, int pos) { return N = N & ~(1 << pos); }
bool check(int N, int pos) { return (bool)(N & (1 << pos)); }
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  int n, m;
  cin >> n >> m;
  vector<int> divs;
  divs.push_back(1);
  for (int i = 2; i <= sqrt(n) + 1; i++) {
    int ii = n / i;
    if (i * ii == n and i <= ii) {
      if (i == ii)
        divs.push_back(i);
      else
        divs.push_back(i), divs.push_back(ii);
    }
  }
  vector<pair<int, int> > vec;
  for (int i = 1; i <= m; i++) {
    int u, v;
    cin >> u >> v;
    u %= n, v %= n;
    vec.push_back(make_pair(min(u, v), max(v, u)));
  }
  sort(vec.begin(), vec.end());
  vector<pair<int, int> > vec1(m);
  for (int div : divs) {
    for (int i = 0; i < m; i++) {
      int u = (vec[i].first + div) % n;
      int v = (vec[i].second + div) % n;
      vec1[i] = make_pair(min(u, v), max(u, v));
    }
    sort(vec1.begin(), vec1.end());
    if (vec1 == vec) {
      cout << "Yes" << endl;
      return 0;
    }
  }
  cout << "No" << endl;
  return 0;
}

### Prompt

Please create a solution in Cpp to the following problem:

Inaka has a disc, the circumference of which is n units. The circumference is equally divided by n points numbered clockwise from 1 to n, such that points i and i + 1 (1 ≤ i < n) are adjacent, and so are points n and 1.

There are m straight segments on the disc, the endpoints of which are all among the aforementioned n points.

Inaka wants to know if her image is rotationally symmetrical, i.e. if there is an integer k (1 ≤ k < n), such that if all segments are rotated clockwise around the center of the circle by k units, the new image will be the same as the original one.

Input

The first line contains two space-separated integers n and m (2 ≤ n ≤ 100 000, 1 ≤ m ≤ 200 000) — the number of points and the number of segments, respectively.

The i-th of the following m lines contains two space-separated integers a_i and b_i (1 ≤ a_i, b_i ≤ n, a_i ≠ b_i) that describe a segment connecting points a_i and b_i.

It is guaranteed that no segments coincide.

Output

Output one line — "Yes" if the image is rotationally symmetrical, and "No" otherwise (both excluding quotation marks).

You can output each letter in any case (upper or lower).

Examples

Input


12 6
1 3
3 7
5 7
7 11
9 11
11 3


Output


Yes


Input


9 6
4 5
5 6
7 8
8 9
1 2
2 3


Output


Yes


Input


10 3
1 2
3 2
7 2


Output


No


Input


10 2
1 6
2 7


Output


Yes

Note

The first two examples are illustrated below. Both images become the same as their respective original ones after a clockwise rotation of 120 degrees around the center.

<image>

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <class T>
class compare {
 public:
  bool operator()(pair<T, T> &x, pair<T, T> &y) {
    if (x.first == y.first) {
      return x.second > y.second;
    }
    return x.first > y.first;
  }
};
template <class T>
ostream &operator<<(ostream &os, const pair<T, T> &a) {
  os << a.first << " " << a.second;
}
template <class T>
void print(vector<T> &vec) {
  for (int i = 1; i < (int)vec.size(); i++) cout << vec[i] << " ";
  cout << endl;
}
template <class T>
void print(set<T> &s) {
  for (auto it : s) cout << it << " ";
  cout << endl;
}
template <class T>
void print(list<T> &lst) {
  for (auto it : lst) cout << it << " ";
  cout << endl;
}
template <class T>
long long power(T a, int b) {
  long long po = 1;
  while (b--) po *= a;
  return po;
}
template <class T>
pair<T, T> operator+(const pair<T, T> &a, const pair<T, T> &b) {
  return {a.first + b.first, a.second + b.second};
}
template <class T>
pair<T, T> operator-(const pair<T, T> &a, const pair<T, T> &b) {
  return {a.first - b.first, a.second - b.second};
}
template <class T>
pair<T, T> operator*(const pair<T, T> &a, const pair<T, T> &b) {
  return {a.first * b.first, a.second * b.second};
}
template <class T>
pair<T, T> operator%(const pair<T, T> &a, const pair<T, T> &b) {
  return {a.first % b.first, a.second % b.second};
}
template <class T, class U>
pair<T, T> operator+(const pair<T, T> &a, const U &b) {
  return {a.first + b, a.second + b};
}
template <class T, class U>
pair<T, T> operator*(const pair<T, T> &a, const U &b) {
  return {a.first * b, a.second * b};
}
int Set(int N, int pos) { return N = N | (1 << pos); }
int reset(int N, int pos) { return N = N & ~(1 << pos); }
bool check(int N, int pos) { return (bool)(N & (1 << pos)); }
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  int n, m;
  cin >> n >> m;
  vector<int> divs;
  divs.push_back(1);
  for (int i = 2; i <= sqrt(n) + 1; i++) {
    int ii = n / i;
    if (i * ii == n and i <= ii) {
      if (i == ii)
        divs.push_back(i);
      else
        divs.push_back(i), divs.push_back(ii);
    }
  }
  vector<pair<int, int> > vec;
  for (int i = 1; i <= m; i++) {
    int u, v;
    cin >> u >> v;
    u %= n, v %= n;
    vec.push_back(make_pair(min(u, v), max(v, u)));
  }
  sort(vec.begin(), vec.end());
  vector<pair<int, int> > vec1(m);
  for (int div : divs) {
    for (int i = 0; i < m; i++) {
      int u = (vec[i].first + div) % n;
      int v = (vec[i].second + div) % n;
      vec1[i] = make_pair(min(u, v), max(u, v));
    }
    sort(vec1.begin(), vec1.end());
    if (vec1 == vec) {
      cout << "Yes" << endl;
      return 0;
    }
  }
  cout << "No" << endl;
  return 0;
}

```