#include <bits/stdc++.h>
using namespace std;
const long long maxn = 5e5 + 5;
void getZarr(vector<int>& str, int Z[]) {
  int n = str.size();
  int L, R, k;
  L = R = 0;
  for (int i = 1; i < n / 2 + 1; ++i) {
    if (i > R) {
      int l = i, r = i;
      while (r < n && str[r - l] == str[r]) r++;
      Z[i] = r - l;
      r--;
      if (Z[i] > 0) {
        R = r;
        L = l;
      }
    } else {
      k = i - L;
      if (Z[k] < R - i + 1)
        Z[i] = Z[k];
      else if (Z[k] > R - i + 1)
        Z[i] = R - i + 1;
      else {
        L = i;
        R++;
        while (R < n && str[R] == str[R - L]) R++;
        Z[i] = R - L;
        R--;
      }
    }
  }
}
inline int clockwise(int a, int b, int n) {
  if (a < b) {
    return b - a;
  }
  return n - (a - b);
}
int main() {
  int n, m;
  cin >> n >> m;
  vector<vector<int> > v(n);
  for (int(i) = 0; (i) < (m); (i)++) {
    int a, b;
    cin >> a >> b;
    a--;
    b--;
    v[a].push_back(clockwise(a, b, n));
    v[b].push_back(clockwise(b, a, n));
  }
  for (int(i) = 0; (i) < (n); (i)++) sort((v[i]).begin(), (v[i]).end());
  vector<int> zstr;
  for (auto it : v) {
    for (auto it1 : it) {
      zstr.push_back(it1);
    }
    zstr.push_back(-1);
  }
  int x = zstr.size();
  for (int(i) = 0; (i) < (x); (i)++) zstr.push_back(zstr[i]);
  int z[maxn];
  getZarr(zstr, z);
  for (int(i) = 0; (i) < (x - 1); (i)++) {
    if (z[i + 1] >= x) {
      cout << "Yes" << endl;
      return 0;
    }
  }
  cout << "No" << endl;
  return 0;
}

### 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;
const long long maxn = 5e5 + 5;
void getZarr(vector<int>& str, int Z[]) {
  int n = str.size();
  int L, R, k;
  L = R = 0;
  for (int i = 1; i < n / 2 + 1; ++i) {
    if (i > R) {
      int l = i, r = i;
      while (r < n && str[r - l] == str[r]) r++;
      Z[i] = r - l;
      r--;
      if (Z[i] > 0) {
        R = r;
        L = l;
      }
    } else {
      k = i - L;
      if (Z[k] < R - i + 1)
        Z[i] = Z[k];
      else if (Z[k] > R - i + 1)
        Z[i] = R - i + 1;
      else {
        L = i;
        R++;
        while (R < n && str[R] == str[R - L]) R++;
        Z[i] = R - L;
        R--;
      }
    }
  }
}
inline int clockwise(int a, int b, int n) {
  if (a < b) {
    return b - a;
  }
  return n - (a - b);
}
int main() {
  int n, m;
  cin >> n >> m;
  vector<vector<int> > v(n);
  for (int(i) = 0; (i) < (m); (i)++) {
    int a, b;
    cin >> a >> b;
    a--;
    b--;
    v[a].push_back(clockwise(a, b, n));
    v[b].push_back(clockwise(b, a, n));
  }
  for (int(i) = 0; (i) < (n); (i)++) sort((v[i]).begin(), (v[i]).end());
  vector<int> zstr;
  for (auto it : v) {
    for (auto it1 : it) {
      zstr.push_back(it1);
    }
    zstr.push_back(-1);
  }
  int x = zstr.size();
  for (int(i) = 0; (i) < (x); (i)++) zstr.push_back(zstr[i]);
  int z[maxn];
  getZarr(zstr, z);
  for (int(i) = 0; (i) < (x - 1); (i)++) {
    if (z[i + 1] >= x) {
      cout << "Yes" << endl;
      return 0;
    }
  }
  cout << "No" << endl;
  return 0;
}

```