#include <bits/stdc++.h>
using namespace std;
const int N = 100005;
void solve() {
  int n, m;
  cin >> n >> m;
  vector<pair<int, int> > l;
  for (int i = 0; i < m; i++) {
    int a, b;
    cin >> a >> b;
    a %= n;
    b %= n;
    l.push_back(make_pair(max(a, b), min(a, b)));
  }
  sort(l.begin(), l.end());
  int t = 0;
  set<int> fact;
  for (int i = 2; i < (int)sqrt(n) + 1; i++) {
    if (n % i == 0) {
      fact.insert(i);
      fact.insert(n / i);
    }
  }
  fact.insert(1);
  for (auto &fi : fact) {
    vector<pair<int, int> > l1;
    int f = 0;
    for (int i = 0; i < m; i++) {
      int a = (l[i].first + fi) % n;
      int b = (l[i].second + fi) % n;
      l1.push_back(make_pair(max(a, b), min(a, b)));
    }
    sort(l1.begin(), l1.end());
    for (int i = 0; i < m; i++) {
      if ((l1[i].first != l[i].first) || (l1[i].second != l[i].second)) {
        f = 1;
        break;
      }
    }
    if (f == 0) {
      t = 1;
      cout << "Yes" << endl;
      break;
    }
  }
  if (t == 0) cout << "No" << endl;
}
int main() {
  cin.sync_with_stdio(false), cin.tie(NULL);
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int t = 1;
  int c = 0;
  while (t--) {
    solve();
    c += 1;
  }
  return 0;
}
