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>
#include <bits/stdc++.h>
using namespace std;
set<pair<int, int> > s;
pair<int, int> ab[200000];
int n, m;
bool rotational(int k) {
  if (k == n) return false;
  bool r = true;
  for (int i = 1; i <= m; i++) {
    int a = ab[i].first;
    int b = ab[i].second;
    a += k;
    b += k;
    if (a > n) {
      a %= n;
      if (a == 0) a = n;
    }
    if (b > n) {
      b %= n;
      if (b == 0) b = n;
    }
    pair<int, int> temp = make_pair(min(a, b), max(a, b));
    if (!s.count(temp)) {
      r = false;
      break;
    }
  }
  return r;
}
int main() {
  cin >> n >> m;
  for (int i = 1; i <= m; i++) {
    int a, b;
    cin >> a >> b;
    pair<int, int> temp = make_pair(min(a, b), max(a, b));
    ab[i] = temp;
    s.insert(temp);
  }
  bool ans = false;
  for (int i = 1; i <= sqrt(n); i++) {
    if (n % i == 0) {
      if (rotational(i)) {
        ans = true;
        break;
      }
      if (rotational(n / i)) {
        ans = true;
        break;
      }
    }
  }
  if (ans) {
    cout << "Yes\n";
  } else {
    cout << "No\n";
  }
}
