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;
const int maxn = 2e5 + 5;
int n, m;
struct KMP {
  vector<vector<int>> s;
  int n;
  vector<int> link;
  void build(vector<vector<int>> t) {
    s = t;
    n = (int)s.size();
    link.resize(n);
    int cur = link[0] = -1;
    for (int i = 1; i < n; i++) {
      while (cur >= 0 && s[i] != s[cur + 1]) cur = link[cur];
      if (s[i] == s[cur + 1]) cur++;
      link[i] = cur;
    }
  }
  vector<int> query(vector<vector<int>> t) {
    vector<int> res;
    int k = (int)t.size();
    int cur = -1;
    for (int i = 0; i < k; i++) {
      while (cur >= 0 && t[i] != s[cur + 1]) cur = link[cur];
      if (t[i] == s[cur + 1]) cur++;
      if (cur == n - 1) {
        res.push_back(i - n + 1);
        cur = link[cur];
      }
    }
    return res;
  }
} kmp;
int cal(int x, int y) {
  if (x > y) swap(x, y);
  return min(y - x, n - y + x);
}
int main() {
  cin >> n >> m;
  vector<vector<int>> a, b;
  a.resize(2 * n - 1);
  b.resize(n);
  for (int i = (0); i < (m); i++) {
    int x, y;
    cin >> x >> y;
    x--;
    y--;
    int dis = cal(x, y);
    a[x].push_back(dis);
    a[y].push_back(dis);
    b[x].push_back(dis);
    b[y].push_back(dis);
  }
  for (int i = (0); i < (n); i++) {
    sort(a[i].begin(), a[i].end());
    sort(b[i].begin(), b[i].end());
  }
  for (int i = (n); i < (2 * n - 1); i++) {
    a[i] = a[i - n];
  }
  kmp.build(b);
  vector<int> res = kmp.query(a);
  if ((int)res.size() > 1)
    cout << "Yes";
  else
    cout << "No";
  return 0;
}
