#include <bits/stdc++.h>
using namespace std;
const long long N = 200001;
long long n, m, t;
map<pair<long long, long long>, long long> h;
vector<long long> v;
vector<pair<long long, long long> > s;
int main() {
  std::ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> m;
  for (int i = 0; i < m; i++) {
    long long a, b;
    cin >> a >> b;
    pair<long long, long long> p, d;
    p.first = a;
    p.second = b;
    d.first = b;
    d.second = a;
    s.push_back(p);
    h[p] = 1;
    h[d] = 1;
  }
  for (int i = 1; i < n; i++) {
    if (n % i == 0) v.push_back(i);
  }
  long long x = 0;
  for (int i = 0; i < v.size(); i++) {
    t = 0;
    for (int j = 0; j < m; j++) {
      long long a, b;
      a = s[j].first;
      b = s[j].second;
      pair<long long, long long> c;
      c.first = (a + v[i]) % n;
      c.second = (b + v[i]) % n;
      if (c.first == 0) c.first = n;
      if (c.second == 0) c.second = n;
      if (h[c] == 0) {
        t = 1;
        break;
      }
    }
    if (t == 0) {
      x = 1;
      break;
    }
  }
  if (x == 1)
    cout << "Yes";
  else
    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;
const long long N = 200001;
long long n, m, t;
map<pair<long long, long long>, long long> h;
vector<long long> v;
vector<pair<long long, long long> > s;
int main() {
  std::ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> m;
  for (int i = 0; i < m; i++) {
    long long a, b;
    cin >> a >> b;
    pair<long long, long long> p, d;
    p.first = a;
    p.second = b;
    d.first = b;
    d.second = a;
    s.push_back(p);
    h[p] = 1;
    h[d] = 1;
  }
  for (int i = 1; i < n; i++) {
    if (n % i == 0) v.push_back(i);
  }
  long long x = 0;
  for (int i = 0; i < v.size(); i++) {
    t = 0;
    for (int j = 0; j < m; j++) {
      long long a, b;
      a = s[j].first;
      b = s[j].second;
      pair<long long, long long> c;
      c.first = (a + v[i]) % n;
      c.second = (b + v[i]) % n;
      if (c.first == 0) c.first = n;
      if (c.second == 0) c.second = n;
      if (h[c] == 0) {
        t = 1;
        break;
      }
    }
    if (t == 0) {
      x = 1;
      break;
    }
  }
  if (x == 1)
    cout << "Yes";
  else
    cout << "No";
  return 0;
}

```