#include <bits/stdc++.h>
using namespace std;
int main() {
  long long xx, yy, n, m, i, g, j, k, x, y;
  std::vector<long long> v;
  vector<pair<long long, long long>> vp;
  cin >> n >> m;
  map<pair<long long, long long>, long long> mp;
  for (i = 0; i < m; i++) {
    cin >> x >> y;
    vp.push_back({x, y});
    mp[{x, y}]++;
  }
  for (i = 1; i * i <= n; i++) {
    if (n % i == 0) {
      v.push_back(i);
      v.push_back(n / i);
    }
    if ((n % i == 0 && i == n / i) || i == 1) {
      v.pop_back();
    }
  }
  for (auto itr : v) {
    g = 1;
    k = itr;
    for (i = 0; i < m; i++) {
      xx = vp[i].first + k;
      yy = vp[i].second + k;
      if (xx >= n + 1) {
        xx = xx % (n + 1) + 1;
      }
      if (yy >= n + 1) {
        yy = yy % (n + 1) + 1;
      }
      if (mp.find({xx, yy}) == mp.end() && mp.find({yy, xx}) == mp.end()) {
        g = 0;
        break;
      }
    }
    if (g) {
      cout << "Yes"
           << "\n";
      return 0;
    }
  }
  cout << "No"
       << "\n";
  return 0;
}

### Prompt

In Cpp, your task is to solve the following problem:

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>

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int main() {
  long long xx, yy, n, m, i, g, j, k, x, y;
  std::vector<long long> v;
  vector<pair<long long, long long>> vp;
  cin >> n >> m;
  map<pair<long long, long long>, long long> mp;
  for (i = 0; i < m; i++) {
    cin >> x >> y;
    vp.push_back({x, y});
    mp[{x, y}]++;
  }
  for (i = 1; i * i <= n; i++) {
    if (n % i == 0) {
      v.push_back(i);
      v.push_back(n / i);
    }
    if ((n % i == 0 && i == n / i) || i == 1) {
      v.pop_back();
    }
  }
  for (auto itr : v) {
    g = 1;
    k = itr;
    for (i = 0; i < m; i++) {
      xx = vp[i].first + k;
      yy = vp[i].second + k;
      if (xx >= n + 1) {
        xx = xx % (n + 1) + 1;
      }
      if (yy >= n + 1) {
        yy = yy % (n + 1) + 1;
      }
      if (mp.find({xx, yy}) == mp.end() && mp.find({yy, xx}) == mp.end()) {
        g = 0;
        break;
      }
    }
    if (g) {
      cout << "Yes"
           << "\n";
      return 0;
    }
  }
  cout << "No"
       << "\n";
  return 0;
}

```