#include <bits/stdc++.h>
using namespace std;
void __print(int x) { cout << x; }
void __print(long x) { cout << x; }
void __print(long long x) { cout << x; }
void __print(unsigned x) { cout << x; }
void __print(unsigned long x) { cout << x; }
void __print(unsigned long long x) { cout << x; }
void __print(float x) { cout << x; }
void __print(double x) { cout << x; }
void __print(long double x) { cout << x; }
void __print(char x) { cout << '\'' << x << '\''; }
void __print(const char *x) { cout << '\"' << x << '\"'; }
void __print(const string &x) { cout << '\"' << x << '\"'; }
void __print(bool x) { cout << (x ? "true" : "false"); }
template <typename T, typename V>
void __print(const pair<T, V> &x) {
  cout << '{';
  __print(x.first);
  cout << ',';
  __print(x.second);
  cout << '}';
}
template <typename T>
void __print(const T &x) {
  int f = 0;
  cout << '{';
  for (auto &i : x) cout << (f++ ? "," : ""), __print(i);
  cout << "}";
}
void _print() { cout << "\n"; }
template <typename T, typename... V>
void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v)) cout << ", ";
  _print(v...);
}
vector<pair<int, int>> v;
int n, m;
bool check(int oops) {
  if (oops == n) return false;
  vector<pair<int, int>> t;
  for (int i = (0); i < (m); ++i) {
    t.push_back(make_pair(v[i].first, v[i].second));
    t[i].first = (v[i].first + oops) % n;
    t[i].second = (v[i].second + oops) % n;
    if (t[i].first > t[i].second) swap(t[i].first, t[i].second);
  }
  sort(begin(t), end(t));
  if (t == v) return true;
  return false;
}
int solve() {
  cin >> n >> m;
  for (int i = (0); i < (m); ++i) {
    int x, y;
    cin >> x >> y;
    x %= n;
    y %= n;
    if (x > y) swap(x, y);
    v.push_back(make_pair(x, y));
  }
  sort(begin(v), end(v));
  for (int i = 1; i <= sqrt(n); i++) {
    if (n % i) continue;
    if (check(i) or check(n / i)) return cout << "Yes", 0;
  }
  cout << "No";
  return 0;
}
int main() {
  ios_base::sync_with_stdio(NULL);
  cin.tie(NULL);
  cout.tie(NULL);
  int t = 1;
  while (t--) {
    solve();
  }
  return 0;
}

### Prompt

In CPP, your task is to solve 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;
void __print(int x) { cout << x; }
void __print(long x) { cout << x; }
void __print(long long x) { cout << x; }
void __print(unsigned x) { cout << x; }
void __print(unsigned long x) { cout << x; }
void __print(unsigned long long x) { cout << x; }
void __print(float x) { cout << x; }
void __print(double x) { cout << x; }
void __print(long double x) { cout << x; }
void __print(char x) { cout << '\'' << x << '\''; }
void __print(const char *x) { cout << '\"' << x << '\"'; }
void __print(const string &x) { cout << '\"' << x << '\"'; }
void __print(bool x) { cout << (x ? "true" : "false"); }
template <typename T, typename V>
void __print(const pair<T, V> &x) {
  cout << '{';
  __print(x.first);
  cout << ',';
  __print(x.second);
  cout << '}';
}
template <typename T>
void __print(const T &x) {
  int f = 0;
  cout << '{';
  for (auto &i : x) cout << (f++ ? "," : ""), __print(i);
  cout << "}";
}
void _print() { cout << "\n"; }
template <typename T, typename... V>
void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v)) cout << ", ";
  _print(v...);
}
vector<pair<int, int>> v;
int n, m;
bool check(int oops) {
  if (oops == n) return false;
  vector<pair<int, int>> t;
  for (int i = (0); i < (m); ++i) {
    t.push_back(make_pair(v[i].first, v[i].second));
    t[i].first = (v[i].first + oops) % n;
    t[i].second = (v[i].second + oops) % n;
    if (t[i].first > t[i].second) swap(t[i].first, t[i].second);
  }
  sort(begin(t), end(t));
  if (t == v) return true;
  return false;
}
int solve() {
  cin >> n >> m;
  for (int i = (0); i < (m); ++i) {
    int x, y;
    cin >> x >> y;
    x %= n;
    y %= n;
    if (x > y) swap(x, y);
    v.push_back(make_pair(x, y));
  }
  sort(begin(v), end(v));
  for (int i = 1; i <= sqrt(n); i++) {
    if (n % i) continue;
    if (check(i) or check(n / i)) return cout << "Yes", 0;
  }
  cout << "No";
  return 0;
}
int main() {
  ios_base::sync_with_stdio(NULL);
  cin.tie(NULL);
  cout.tie(NULL);
  int t = 1;
  while (t--) {
    solve();
  }
  return 0;
}

```