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>
#include <bits/stdc++.h>
template <class C, class E>
inline bool contains(const C& container, const E& element) {
  return container.find(element) != container.end();
}
template <class T>
inline void checkmin(T& a, T b) {
  if (b < a) a = b;
}
template <class T>
inline void checkmax(T& a, T b) {
  if (b > a) a = b;
}
using namespace std;
int n, m;
vector<vector<int>> salenDe;
int DistFrom(int a, int b) {
  if (b > a)
    return b - a;
  else
    return n - (a - b);
}
map<vector<int>, int> chars;
using namespace std;
void preKMP(vector<int> pattern, vector<int>& f) {
  int m = pattern.size(), k;
  f[0] = -1;
  for (int i = 1; i < m; i++) {
    k = f[i - 1];
    while (k >= 0) {
      if (pattern[k] == pattern[i - 1])
        break;
      else
        k = f[k];
    }
    f[i] = k + 1;
  }
}
bool KMP(vector<int> pattern, vector<int> target) {
  int m = pattern.size();
  int n = target.size();
  vector<int> f(m);
  preKMP(pattern, f);
  int i = 0;
  int k = 0;
  while (i < n) {
    if (k == -1) {
      i++;
      k = 0;
    } else if (target[i] == pattern[k]) {
      i++;
      k++;
      if (k == m) return 1;
    } else
      k = f[k];
  }
  return 0;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  cout << std::setprecision(15);
  cout << std::fixed;
  cin >> n >> m;
  salenDe.resize(n);
  for (int i = (0), _b = ((m)-1); i <= _b; i++) {
    int a, b;
    cin >> a >> b;
    --a;
    --b;
    salenDe[a].push_back(DistFrom(a, b));
    salenDe[b].push_back(DistFrom(b, a));
  }
  int nextC = 1;
  vector<int> salenDeC(n);
  vector<int> salenDeCiclic(n * 2 - 2);
  for (int i = (0), _b = ((n)-1); i <= _b; i++) {
    sort((salenDe[i]).begin(), (salenDe[i]).end());
    auto it = chars.find(salenDe[i]);
    if (it == chars.end()) chars[salenDe[i]] = nextC++;
    int cc = chars[salenDe[i]];
    salenDeC[i] = cc;
  }
  for (int i = (0), _b = ((salenDeCiclic.size()) - 1); i <= _b; i++)
    salenDeCiclic[i] = salenDeC[(i + 1) % n];
  if (KMP(salenDeC, salenDeCiclic))
    cout << "Yes";
  else
    cout << "No";
  return 0;
}
