#include <bits/stdc++.h>
using namespace std;
struct S {
  int l, r;
} a[200010];
map<int, map<int, int> > mp;
int main() {
  int n, m, i, j;
  cin >> n >> m;
  for (i = 0; i < m; i++) {
    cin >> a[i].l >> a[i].r;
    mp[a[i].l][a[i].r] = 1;
    mp[a[i].r][a[i].l] = 1;
  }
  int fll = 0;
  for (i = 1; i <= sqrt(n + 0.5); i++) {
    if (n % i == 0) {
      int c = i;
      int fl = 0;
      for (j = 0; j < m; j++) {
        int x = (a[j].l + c) % n, y = (a[j].r + c) % n;
        if (x == 0) x = n;
        if (y == 0) y = n;
        if (mp[x][y] == 0) {
          fl = 1;
          break;
        }
      }
      if (fl == 0) {
        fll = 1;
        break;
      }
      if (i == 1) continue;
      c = n / i;
      fl = 0;
      for (j = 0; j < m; j++) {
        int x = (a[j].l + c) % n, y = (a[j].r + c) % n;
        if (x == 0) x = n;
        if (y == 0) y = n;
        if (mp[x][y] == 0) {
          fl = 1;
          break;
        }
      }
      if (fl == 0) {
        fll = 1;
        break;
      }
    }
    if (fll == 1) break;
  }
  if (fll == 1)
    cout << "YES";
  else
    cout << "NO";
}

### Prompt

Your challenge is to write 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;
struct S {
  int l, r;
} a[200010];
map<int, map<int, int> > mp;
int main() {
  int n, m, i, j;
  cin >> n >> m;
  for (i = 0; i < m; i++) {
    cin >> a[i].l >> a[i].r;
    mp[a[i].l][a[i].r] = 1;
    mp[a[i].r][a[i].l] = 1;
  }
  int fll = 0;
  for (i = 1; i <= sqrt(n + 0.5); i++) {
    if (n % i == 0) {
      int c = i;
      int fl = 0;
      for (j = 0; j < m; j++) {
        int x = (a[j].l + c) % n, y = (a[j].r + c) % n;
        if (x == 0) x = n;
        if (y == 0) y = n;
        if (mp[x][y] == 0) {
          fl = 1;
          break;
        }
      }
      if (fl == 0) {
        fll = 1;
        break;
      }
      if (i == 1) continue;
      c = n / i;
      fl = 0;
      for (j = 0; j < m; j++) {
        int x = (a[j].l + c) % n, y = (a[j].r + c) % n;
        if (x == 0) x = n;
        if (y == 0) y = n;
        if (mp[x][y] == 0) {
          fl = 1;
          break;
        }
      }
      if (fl == 0) {
        fll = 1;
        break;
      }
    }
    if (fll == 1) break;
  }
  if (fll == 1)
    cout << "YES";
  else
    cout << "NO";
}

```