#include <bits/stdc++.h>
using namespace std;
vector<pair<int, int> > a;
int n, k;
bool teste(int v) {
  vector<pair<int, int> > vet;
  for (auto &it : a) {
    int v1 = (it.first + v) % n;
    int v2 = (it.second + v) % n;
    if (v1 > v2) swap(v1, v2);
    vet.emplace_back(v1, v2);
  }
  sort(vet.begin(), vet.end());
  return vet == a;
}
int main() {
  cin >> n >> k;
  int v1, v2;
  for (int i = 0; i < k; i++) {
    cin >> v1 >> v2;
    v1--;
    v2--;
    if (v1 > v2) swap(v1, v2);
    a.push_back({v1, v2});
  }
  sort(a.begin(), a.end());
  bool f = 0;
  for (int i = 1; i * i <= n; i++) {
    if (n % i == 0) {
      f = teste(i);
      if (f) break;
      if (i == 1) continue;
      f = teste(n / i);
      if (f) break;
    }
  }
  if (f)
    cout << "YES";
  else
    cout << "NO";
}

### Prompt

Your task is to create 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;
vector<pair<int, int> > a;
int n, k;
bool teste(int v) {
  vector<pair<int, int> > vet;
  for (auto &it : a) {
    int v1 = (it.first + v) % n;
    int v2 = (it.second + v) % n;
    if (v1 > v2) swap(v1, v2);
    vet.emplace_back(v1, v2);
  }
  sort(vet.begin(), vet.end());
  return vet == a;
}
int main() {
  cin >> n >> k;
  int v1, v2;
  for (int i = 0; i < k; i++) {
    cin >> v1 >> v2;
    v1--;
    v2--;
    if (v1 > v2) swap(v1, v2);
    a.push_back({v1, v2});
  }
  sort(a.begin(), a.end());
  bool f = 0;
  for (int i = 1; i * i <= n; i++) {
    if (n % i == 0) {
      f = teste(i);
      if (f) break;
      if (i == 1) continue;
      f = teste(n / i);
      if (f) break;
    }
  }
  if (f)
    cout << "YES";
  else
    cout << "NO";
}

```