#include <bits/stdc++.h>
using namespace std;
int mod = 1e9 + 7;
inline int uceil(int a, int b) { return (a % b ? a / b + 1 : a / b); }
int dx[8] = {0, 1, 0, -1, 1, -1, 1, -1};
int dy[8] = {-1, 0, 1, 0, 1, 1, -1, -1};
int n;
vector<pair<int, int> > pt;
bool check(int k) {
  if (k == n) return false;
  vector<pair<int, int> > pt2;
  for (auto a : pt) {
    a.first += k;
    if (a.first >= n) a.first -= n;
    a.second += k;
    if (a.second >= n) a.second -= n;
    if (a.first > a.second) swap(a.first, a.second);
    pt2.emplace_back(a);
  }
  sort(pt2.begin(), pt2.end());
  return pt == pt2;
}
void solvetc(int tt) {
  cin >> n;
  int m;
  cin >> m;
  pt.resize(m);
  for (auto &a : pt) {
    cin >> a.first >> a.second;
    a.first--, a.second--;
    if (a.first > a.second) swap(a.first, a.second);
  }
  sort(pt.begin(), pt.end());
  int root = sqrt(n);
  for (int i = 1; i <= root; i++) {
    if (n % i) continue;
    if (check(i) or check(n / i)) {
      cout << "Yes"
           << "\n";
      return;
    }
  }
  cout << "No"
       << "\n";
}
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  ;
  int nn = 1;
  for (int i = 0; i < (int)nn; i++) solvetc(i + 1);
}

### 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;
int mod = 1e9 + 7;
inline int uceil(int a, int b) { return (a % b ? a / b + 1 : a / b); }
int dx[8] = {0, 1, 0, -1, 1, -1, 1, -1};
int dy[8] = {-1, 0, 1, 0, 1, 1, -1, -1};
int n;
vector<pair<int, int> > pt;
bool check(int k) {
  if (k == n) return false;
  vector<pair<int, int> > pt2;
  for (auto a : pt) {
    a.first += k;
    if (a.first >= n) a.first -= n;
    a.second += k;
    if (a.second >= n) a.second -= n;
    if (a.first > a.second) swap(a.first, a.second);
    pt2.emplace_back(a);
  }
  sort(pt2.begin(), pt2.end());
  return pt == pt2;
}
void solvetc(int tt) {
  cin >> n;
  int m;
  cin >> m;
  pt.resize(m);
  for (auto &a : pt) {
    cin >> a.first >> a.second;
    a.first--, a.second--;
    if (a.first > a.second) swap(a.first, a.second);
  }
  sort(pt.begin(), pt.end());
  int root = sqrt(n);
  for (int i = 1; i <= root; i++) {
    if (n % i) continue;
    if (check(i) or check(n / i)) {
      cout << "Yes"
           << "\n";
      return;
    }
  }
  cout << "No"
       << "\n";
}
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  ;
  int nn = 1;
  for (int i = 0; i < (int)nn; i++) solvetc(i + 1);
}

```