#include <bits/stdc++.h>
using namespace std;
int main() {
  long n, m;
  cin >> n >> m;
  long a, b, x, y, d;
  vector<vector<long>> loc(100005);
  for (long i = 0; i < m; i++) {
    cin >> a >> b;
    a--;
    b--;
    x = min(a, b);
    y = max(a, b);
    if (n % 2 == 0) {
      if ((y - x) > n / 2)
        d = x + n - y;
      else
        d = y - x;
    } else {
      if ((y - x) >= n / 2)
        d = n - y + x;
      else
        d = y - x;
    }
    loc[d].push_back(x);
    loc[d].push_back(y);
  }
  vector<vector<long>> dist(100005);
  long cnt = 0;
  for (long i = 0; i < 100005; i++) {
    if (loc[i].size() == 0) continue;
    cnt++;
    sort(loc[i].begin(), loc[i].end());
    for (long j = 0; j < loc[i].size() - 1; j++) {
      dist[i].push_back(loc[i][j + 1] - loc[i][j]);
    }
    dist[i].push_back(loc[i][0] + n - loc[i][loc[i].size() - 1]);
  }
  long k, sum = 0;
  vector<long> rot(100005, 0);
  for (long i = 0; i < n; i++) {
    if (dist[i].size() == 0) continue;
    vector<pair<long, long>> lps(dist[i].size());
    for (long j = 0; j < dist[i].size(); j++) {
      if (j == 0)
        lps[j] = make_pair(0, 0);
      else {
        k = lps[j - 1].first;
        sum = lps[j - 1].second;
        while (dist[i][j] != dist[i][k] && k > 0) {
          sum = lps[k - 1].second;
          k = lps[k - 1].first;
        }
        if (dist[i][j] == dist[i][k]) {
          lps[j] = make_pair(k + 1, sum + dist[i][j]);
        } else {
          lps[j] = make_pair(0, 0);
        }
      }
    }
    k = lps[dist[i].size() - 1].first;
    sum = lps[dist[i].size() - 1].second;
    while (k > 0) {
      rot[sum]++;
      sum = lps[k - 1].second;
      k = lps[k - 1].first;
    }
  }
  bool fp = false;
  for (long i = 0; i < n; i++) {
    if (rot[i] == cnt) {
      fp = true;
      break;
    }
  }
  if (fp)
    cout << "Yes" << endl;
  else
    cout << "No" << endl;
}

### Prompt

Construct a cpp code solution to the problem outlined:

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 n, m;
  cin >> n >> m;
  long a, b, x, y, d;
  vector<vector<long>> loc(100005);
  for (long i = 0; i < m; i++) {
    cin >> a >> b;
    a--;
    b--;
    x = min(a, b);
    y = max(a, b);
    if (n % 2 == 0) {
      if ((y - x) > n / 2)
        d = x + n - y;
      else
        d = y - x;
    } else {
      if ((y - x) >= n / 2)
        d = n - y + x;
      else
        d = y - x;
    }
    loc[d].push_back(x);
    loc[d].push_back(y);
  }
  vector<vector<long>> dist(100005);
  long cnt = 0;
  for (long i = 0; i < 100005; i++) {
    if (loc[i].size() == 0) continue;
    cnt++;
    sort(loc[i].begin(), loc[i].end());
    for (long j = 0; j < loc[i].size() - 1; j++) {
      dist[i].push_back(loc[i][j + 1] - loc[i][j]);
    }
    dist[i].push_back(loc[i][0] + n - loc[i][loc[i].size() - 1]);
  }
  long k, sum = 0;
  vector<long> rot(100005, 0);
  for (long i = 0; i < n; i++) {
    if (dist[i].size() == 0) continue;
    vector<pair<long, long>> lps(dist[i].size());
    for (long j = 0; j < dist[i].size(); j++) {
      if (j == 0)
        lps[j] = make_pair(0, 0);
      else {
        k = lps[j - 1].first;
        sum = lps[j - 1].second;
        while (dist[i][j] != dist[i][k] && k > 0) {
          sum = lps[k - 1].second;
          k = lps[k - 1].first;
        }
        if (dist[i][j] == dist[i][k]) {
          lps[j] = make_pair(k + 1, sum + dist[i][j]);
        } else {
          lps[j] = make_pair(0, 0);
        }
      }
    }
    k = lps[dist[i].size() - 1].first;
    sum = lps[dist[i].size() - 1].second;
    while (k > 0) {
      rot[sum]++;
      sum = lps[k - 1].second;
      k = lps[k - 1].first;
    }
  }
  bool fp = false;
  for (long i = 0; i < n; i++) {
    if (rot[i] == cnt) {
      fp = true;
      break;
    }
  }
  if (fp)
    cout << "Yes" << endl;
  else
    cout << "No" << endl;
}

```