#include <bits/stdc++.h>
using namespace std;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0), cout.tie(0);
  int n, m;
  cin >> n >> m;
  vector<pair<int, int>> seg(m);
  vector<set<int>> was(n + 1);
  for (int i = 0; i < m; ++i) {
    cin >> seg[i].first >> seg[i].second;
    if (seg[i].first > seg[i].second) {
      swap(seg[i].first, seg[i].second);
    }
    was[seg[i].first].insert(seg[i].second);
  }
  auto check = [&](int k) {
    int cnt = 0;
    for (int i = 0; i < m; ++i) {
      int l = seg[i].first + k, r = seg[i].second + k;
      if (l > n) {
        l -= n;
      }
      if (r > n) {
        r -= n;
      }
      if (l > r) {
        swap(l, r);
      }
      cnt += (was[l].find(r) != was[l].end());
    }
    return cnt == m;
  };
  for (int k = 1; k * k <= n; ++k) {
    if (k == 1) {
      if (check(1)) {
        cout << "Yes";
        return 0;
      }
    } else if (n % k == 0) {
      if (check(k)) {
        cout << "Yes";
        return 0;
      } else if (check(n / k)) {
        cout << "Yes";
        return 0;
      }
    }
  }
  cout << "No";
  return 0;
}

### Prompt

Please create a solution in CPP 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;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0), cout.tie(0);
  int n, m;
  cin >> n >> m;
  vector<pair<int, int>> seg(m);
  vector<set<int>> was(n + 1);
  for (int i = 0; i < m; ++i) {
    cin >> seg[i].first >> seg[i].second;
    if (seg[i].first > seg[i].second) {
      swap(seg[i].first, seg[i].second);
    }
    was[seg[i].first].insert(seg[i].second);
  }
  auto check = [&](int k) {
    int cnt = 0;
    for (int i = 0; i < m; ++i) {
      int l = seg[i].first + k, r = seg[i].second + k;
      if (l > n) {
        l -= n;
      }
      if (r > n) {
        r -= n;
      }
      if (l > r) {
        swap(l, r);
      }
      cnt += (was[l].find(r) != was[l].end());
    }
    return cnt == m;
  };
  for (int k = 1; k * k <= n; ++k) {
    if (k == 1) {
      if (check(1)) {
        cout << "Yes";
        return 0;
      }
    } else if (n % k == 0) {
      if (check(k)) {
        cout << "Yes";
        return 0;
      } else if (check(n / k)) {
        cout << "Yes";
        return 0;
      }
    }
  }
  cout << "No";
  return 0;
}

```