#include <bits/stdc++.h>
using namespace std;
int mod = 1e9 + 7;
int min(int a, int b) { return (a < b) ? a : b; }
int max(int a, int b) { return (a > b) ? a : b; }
int fp(int a, int b) {
  if (b == 0) return 1;
  int x = fp(a, b / 2);
  x = (x * x) % mod;
  if (b & 1) x = (x * a) % mod;
  return x;
}
const int N = 100005;
int mp[N] = {0};
int mp2[N];
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int n, m;
  cin >> n >> m;
  vector<array<int, 2>> a(m);
  for (int i = 0; i < m; i++) {
    cin >> a[i][0] >> a[i][1];
    if (a[i][0] > a[i][1]) swap(a[i][0], a[i][1]);
    mp[a[i][0]]++;
    mp[a[i][1]]++;
  }
  sort(a.begin(), a.end());
  for (int i = 1; i < n; i++) {
    if (n % i != 0) continue;
    memset(mp2, 0, sizeof(mp2));
    vector<array<int, 2>> b(m);
    int f = 1;
    for (int j = 0; j < m; j++) {
      int p = a[j][0] + i;
      int q = a[j][1] + i;
      if (p > n) p -= n;
      if (q > n) q -= n;
      if (p > q) swap(p, q);
      mp2[p]++;
      mp2[q]++;
      if (mp2[p] > mp[p] || mp2[q] > mp[q]) {
        f = 0;
        break;
      }
      b[j] = {p, q};
    }
    if (!f) continue;
    sort(b.begin(), b.end());
    if (a == b) {
      cout << "Yes";
      return 0;
    }
  }
  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;
int mod = 1e9 + 7;
int min(int a, int b) { return (a < b) ? a : b; }
int max(int a, int b) { return (a > b) ? a : b; }
int fp(int a, int b) {
  if (b == 0) return 1;
  int x = fp(a, b / 2);
  x = (x * x) % mod;
  if (b & 1) x = (x * a) % mod;
  return x;
}
const int N = 100005;
int mp[N] = {0};
int mp2[N];
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int n, m;
  cin >> n >> m;
  vector<array<int, 2>> a(m);
  for (int i = 0; i < m; i++) {
    cin >> a[i][0] >> a[i][1];
    if (a[i][0] > a[i][1]) swap(a[i][0], a[i][1]);
    mp[a[i][0]]++;
    mp[a[i][1]]++;
  }
  sort(a.begin(), a.end());
  for (int i = 1; i < n; i++) {
    if (n % i != 0) continue;
    memset(mp2, 0, sizeof(mp2));
    vector<array<int, 2>> b(m);
    int f = 1;
    for (int j = 0; j < m; j++) {
      int p = a[j][0] + i;
      int q = a[j][1] + i;
      if (p > n) p -= n;
      if (q > n) q -= n;
      if (p > q) swap(p, q);
      mp2[p]++;
      mp2[q]++;
      if (mp2[p] > mp[p] || mp2[q] > mp[q]) {
        f = 0;
        break;
      }
      b[j] = {p, q};
    }
    if (!f) continue;
    sort(b.begin(), b.end());
    if (a == b) {
      cout << "Yes";
      return 0;
    }
  }
  cout << "No";
}

```