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>
using namespace std;
template <typename Arg1>
void __f(const char* name, Arg1&& arg1) {
  cerr << name << " : " << arg1 << '\n';
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args) {
  const char* comma = strchr(names + 1, ',');
  cerr.write(names, comma - names) << " : " << arg1 << " | ";
  __f(comma + 1, args...);
}
const long long int N = 100005;
vector<long long int> gived(long long int n) {
  vector<long long int> v;
  for (long long int i = 1; i < n; i++) {
    if (n % i == 0) {
      v.push_back(i);
    }
  }
  return v;
}
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  {
    long long int i, j, k, n, m, ans = 0, cnt = 0, sum = 0;
    cin >> n >> m;
    vector<pair<long long int, long long int> > a(m), vv(m);
    set<pair<long long int, long long int> > St;
    for (i = 0; i < m; i++) {
      cin >> a[i].first >> a[i].second;
      a[i].first--;
      a[i].second--;
      if (a[i].first > a[i].second) {
        swap(a[i].first, a[i].second);
      }
      vv[i] = {a[i].first, a[i].second};
    }
    vector<long long int> v = gived(n);
    sort(vv.begin(), vv.end());
    for (auto x : v) {
      for (i = 0; i < m; i++) {
        pair<long long int, long long int> p = {
            min((a[i].first + x) % n, (a[i].second + x) % n),
            max((a[i].first + x) % n, (a[i].second + x) % n)};
        bool bl = binary_search(vv.begin(), vv.end(), p);
        if (!bl) {
          break;
        }
      }
      if (i == m) {
        cout << "Yes";
        return 0;
      }
    }
    cout << "No";
  }
}
