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;
const int N = 1e5 + 5;
int n, m;
set<pair<int, int> > S;
bool check(int add) {
  for (auto it : S) {
    int i = (it.first + add) % n;
    int j = (it.second + add) % n;
    if (i > j) swap(i, j);
    if (S.find({i, j}) == S.end()) return false;
  }
  return true;
}
int main() {
  ios ::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  if (fopen("main.in", "r"))
    freopen("main.in", "r", stdin);
  else if (fopen("something"
                 ".inp",
                 "r"))
    freopen(
        "something"
        ".inp",
        "r", stdin),
        freopen(
            "something"
            ".out",
            "w", stdout);
  cin >> n >> m;
  for (int i = 1; i <= m; i++) {
    int a, b;
    cin >> a >> b;
    a--;
    b--;
    if (a > b) swap(a, b);
    S.insert({a, b});
  }
  for (int i = 1; i < n; i++)
    if (n % i == 0)
      if (check(i)) {
        cout << "YES\n";
        exit(0);
      }
  cout << "NO\n";
  return 0;
}
