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;
inline long long read() {
  long long f = 1, x = 0;
  char ch = getchar();
  while (!isdigit(ch)) {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (isdigit(ch)) {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * f;
}
const int MAXN = 2e5 + 5;
int n, m;
map<pair<int, int>, bool> mp;
pair<int, int> p[MAXN];
bool check(int k) {
  if (k >= n) return false;
  for (int i = 1; i <= m; ++i) {
    pair<int, int> t;
    t.first = p[i].first + k;
    t.second = p[i].second + k;
    if (t.first > n) t.first -= n;
    if (t.second > n) t.second -= n;
    if (t.first > t.second) swap(t.first, t.second);
    if (mp.find(t) == mp.end()) return false;
  }
  return true;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  n = read();
  m = read();
  for (int i = 1; i <= m; ++i) {
    p[i].first = read();
    p[i].second = read();
    if (p[i].first > p[i].second) swap(p[i].first, p[i].second);
    mp[p[i]] = 1;
  }
  for (int i = 1; i * i <= n; ++i) {
    if (n % i) continue;
    if (check(i)) {
      cout << "Yes" << endl;
      return 0;
    }
    if (check(n / i)) {
      cout << "Yes" << endl;
      return 0;
    }
  }
  cout << "No" << endl;
  return 0;
}
