#include <bits/stdc++.h>
using namespace std;
using ll = long long;
int main() {
  cin.sync_with_stdio(false);
  cin.tie(0);
  ll n, m;
  vector<pair<int, int> > arr;
  set<pair<int, int> > s;
  cin >> n >> m;
  while (m--) {
    int x, y;
    cin >> x >> y;
    if (x > y) swap(x, y);
    arr.emplace_back(make_pair(x, y));
    s.insert(make_pair(x, y));
  }
  bool ans = false;
  for (int i = 1; i < n && !ans; ++i) {
    if (n % i == 0) {
      bool flag = true;
      for (auto p : arr) {
        int x, y;
        x = p.first;
        y = p.second;
        x += i;
        y += i;
        while (x > n) x -= n;
        while (y > n) y -= n;
        if (x > y) swap(x, y);
        if (s.count(make_pair(x, y)) == 0) {
          flag = false;
          break;
        }
      }
      ans = flag;
    }
  }
  cout << (ans ? "Yes" : "No") << endl;
}

### Prompt

Generate a cpp solution to 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;
using ll = long long;
int main() {
  cin.sync_with_stdio(false);
  cin.tie(0);
  ll n, m;
  vector<pair<int, int> > arr;
  set<pair<int, int> > s;
  cin >> n >> m;
  while (m--) {
    int x, y;
    cin >> x >> y;
    if (x > y) swap(x, y);
    arr.emplace_back(make_pair(x, y));
    s.insert(make_pair(x, y));
  }
  bool ans = false;
  for (int i = 1; i < n && !ans; ++i) {
    if (n % i == 0) {
      bool flag = true;
      for (auto p : arr) {
        int x, y;
        x = p.first;
        y = p.second;
        x += i;
        y += i;
        while (x > n) x -= n;
        while (y > n) y -= n;
        if (x > y) swap(x, y);
        if (s.count(make_pair(x, y)) == 0) {
          flag = false;
          break;
        }
      }
      ans = flag;
    }
  }
  cout << (ans ? "Yes" : "No") << endl;
}

```