#include <bits/stdc++.h>
using namespace std;
set<pair<long long, long long>> sett;
long long n, m;
bool func(long long k) {
  set<pair<long long, long long>>::iterator it = sett.begin();
  while (it != sett.end()) {
    pair<long long, long long> o = (*it);
    o.first += k;
    o.second += k;
    o.first %= n;
    o.second %= n;
    long long f = o.first;
    long long ff = o.second;
    o.first = min(f, ff);
    o.second = max(f, ff);
    set<pair<long long, long long>>::iterator it1 = sett.find(o);
    if (it1 == sett.end()) {
      return 0;
    }
    it++;
  }
  return 1;
}
signed main() {
  cin >> n >> m;
  for (long long g = 0; g < m; g++) {
    long long a, b;
    cin >> a >> b;
    a--;
    b--;
    pair<long long, long long> u;
    u.first = min(a, b);
    u.second = max(a, b);
    sett.insert(u);
  }
  for (long long i = 1; i < n; i++) {
    if (n % i == 0) {
      bool d = func(i);
      if (d == 1) {
        cout << "Yes" << endl;
        return 0;
      }
    }
  }
  cout << "No" << endl;
}

### Prompt

In cpp, your task is to solve 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;
set<pair<long long, long long>> sett;
long long n, m;
bool func(long long k) {
  set<pair<long long, long long>>::iterator it = sett.begin();
  while (it != sett.end()) {
    pair<long long, long long> o = (*it);
    o.first += k;
    o.second += k;
    o.first %= n;
    o.second %= n;
    long long f = o.first;
    long long ff = o.second;
    o.first = min(f, ff);
    o.second = max(f, ff);
    set<pair<long long, long long>>::iterator it1 = sett.find(o);
    if (it1 == sett.end()) {
      return 0;
    }
    it++;
  }
  return 1;
}
signed main() {
  cin >> n >> m;
  for (long long g = 0; g < m; g++) {
    long long a, b;
    cin >> a >> b;
    a--;
    b--;
    pair<long long, long long> u;
    u.first = min(a, b);
    u.second = max(a, b);
    sett.insert(u);
  }
  for (long long i = 1; i < n; i++) {
    if (n % i == 0) {
      bool d = func(i);
      if (d == 1) {
        cout << "Yes" << endl;
        return 0;
      }
    }
  }
  cout << "No" << endl;
}

```