#include <bits/stdc++.h>
using namespace std;
inline int read() {
  char ch = getchar();
  int nega = 1;
  while (!isdigit(ch)) {
    if (ch == '-') nega = -1;
    ch = getchar();
  }
  int ans = 0;
  while (isdigit(ch)) {
    ans = ans * 10 + ch - 48;
    ch = getchar();
  }
  if (nega == -1) return -ans;
  return ans;
}
int l[200005], r[200005];
map<pair<int, int>, bool> a;
int n, m;
signed main() {
  cin >> n >> m;
  for (int i = 1; i <= m; i++) {
    l[i] = read(), r[i] = read();
    a[make_pair(l[i] % n, r[i] % n)] = 1;
    a[make_pair(r[i] % n, l[i] % n)] = 1;
  }
  for (int i = 1; i <= n / 2; i++) {
    if (n % i == 0) {
      bool ok = 1;
      for (int j = 1; j <= m; j++) {
        if (a[make_pair((l[j] + i) % n, (r[j] + i) % n)] == 0) {
          ok = false;
          break;
        }
      }
      if (ok) {
        cout << "Yes\n";
        return 0;
      }
    }
  }
  cout << "No\n";
  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;
inline int read() {
  char ch = getchar();
  int nega = 1;
  while (!isdigit(ch)) {
    if (ch == '-') nega = -1;
    ch = getchar();
  }
  int ans = 0;
  while (isdigit(ch)) {
    ans = ans * 10 + ch - 48;
    ch = getchar();
  }
  if (nega == -1) return -ans;
  return ans;
}
int l[200005], r[200005];
map<pair<int, int>, bool> a;
int n, m;
signed main() {
  cin >> n >> m;
  for (int i = 1; i <= m; i++) {
    l[i] = read(), r[i] = read();
    a[make_pair(l[i] % n, r[i] % n)] = 1;
    a[make_pair(r[i] % n, l[i] % n)] = 1;
  }
  for (int i = 1; i <= n / 2; i++) {
    if (n % i == 0) {
      bool ok = 1;
      for (int j = 1; j <= m; j++) {
        if (a[make_pair((l[j] + i) % n, (r[j] + i) % n)] == 0) {
          ok = false;
          break;
        }
      }
      if (ok) {
        cout << "Yes\n";
        return 0;
      }
    }
  }
  cout << "No\n";
  return 0;
}

```