#include <bits/stdc++.h>
using namespace std;
bool chk(map<pair<int, int>, int> &mp, int k, int n) {
  map<pair<int, int>, int> mp2;
  map<pair<int, int>, int>::iterator itr = mp.begin();
  while (itr != mp.end()) {
    int x = ((itr->first).first + k) % n, y = ((itr->first).second + k) % n;
    if (x < y)
      mp2.insert({{x, y}, 0});
    else
      mp2.insert({{y, x}, 0});
    itr++;
  }
  if (mp == mp2)
    return 1;
  else
    return 0;
}
int main() {
  ios_base::sync_with_stdio(false);
  ;
  int n, m;
  cin >> n >> m;
  map<pair<int, int>, int> mp;
  for (int i = 0; i < m; i++) {
    int x, y;
    cin >> x >> y;
    x--, y--;
    if (x < y)
      mp.insert({{x, y}, 0});
    else
      mp.insert({{y, x}, 0});
  }
  for (int i = 2; i < n + 1; i++) {
    int p = 1;
    for (int j = 2; j < int(sqrt(i)) + 1; j++)
      if (i % j == 0) p = 0;
    if (p == 1 && n % i == 0) {
      if (chk(mp, n / i, n) == 1) {
        cout << "YES";
        return 0;
      }
    }
  }
  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;
bool chk(map<pair<int, int>, int> &mp, int k, int n) {
  map<pair<int, int>, int> mp2;
  map<pair<int, int>, int>::iterator itr = mp.begin();
  while (itr != mp.end()) {
    int x = ((itr->first).first + k) % n, y = ((itr->first).second + k) % n;
    if (x < y)
      mp2.insert({{x, y}, 0});
    else
      mp2.insert({{y, x}, 0});
    itr++;
  }
  if (mp == mp2)
    return 1;
  else
    return 0;
}
int main() {
  ios_base::sync_with_stdio(false);
  ;
  int n, m;
  cin >> n >> m;
  map<pair<int, int>, int> mp;
  for (int i = 0; i < m; i++) {
    int x, y;
    cin >> x >> y;
    x--, y--;
    if (x < y)
      mp.insert({{x, y}, 0});
    else
      mp.insert({{y, x}, 0});
  }
  for (int i = 2; i < n + 1; i++) {
    int p = 1;
    for (int j = 2; j < int(sqrt(i)) + 1; j++)
      if (i % j == 0) p = 0;
    if (p == 1 && n % i == 0) {
      if (chk(mp, n / i, n) == 1) {
        cout << "YES";
        return 0;
      }
    }
  }
  cout << "NO";
  return 0;
}

```