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;
vector<long long> z_function(vector<long long> second) {
  long long n = (long long)second.size();
  vector<long long> z(n);
  for (long long i = 1, l = 0, r = 0; i < n; ++i) {
    if (i <= r) z[i] = min(r - i + 1, z[i - l]);
    while (i + z[i] < n && second[z[i]] == second[i + z[i]]) ++z[i];
    if (i + z[i] - 1 > r) l = i, r = i + z[i] - 1;
  }
  return z;
}
signed main() {
  long long n, k;
  cin >> n >> k;
  vector<long long> adj[n + 1];
  for (long long i = 0; i < k; i++) {
    long long p, q;
    cin >> p >> q;
    if (p < q) swap(q, p);
    adj[p].push_back(q - p + n);
    adj[q].push_back(p - q);
  }
  for (long long i = 1; i <= n; i++) sort(adj[i].begin(), adj[i].end());
  vector<long long> str;
  for (long long i = 1; i <= n; i++) {
    for (auto u : adj[i]) str.push_back(u);
    str.push_back(-1);
  }
  long long tmp = str.size();
  for (long long i = 0; i < tmp; i++) {
    str.push_back(str[i]);
  }
  vector<long long> ans = z_function(str);
  for (long long i = 1; i < tmp - 1; i++) {
    if (ans[i] >= tmp) {
      cout << "Yes\n";
      return 0;
    }
  }
  cout << "No\n";
  return 0;
}
