#include <bits/stdc++.h>
using namespace std;
vector<string> vec_splitter(string s) {
  for (char& c : s) c = c == ',' ? ' ' : c;
  stringstream ss;
  ss << s;
  vector<string> res;
  for (string z; ss >> z; res.push_back(z))
    ;
  return res;
}
void debug_out(vector<string> args, int idx) { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(vector<string> args, int idx, Head H, Tail... T) {
  if (idx > 0) cerr << ", ";
  stringstream ss;
  ss << H;
  cerr << args[idx] << " = " << ss.str();
  debug_out(args, idx + 1, T...);
}
void localTest() {}
const long long N = 1e5 + 5;
vector<long long> V[N], G[N];
long long n, m;
bool check(long long x) {
  if (x == n) {
    return 0;
  }
  for (long long i = 0; i < n; ++i) {
    G[i].clear();
    sort((V[i]).begin(), (V[i]).end());
  }
  for (long long i = 0; i < n; ++i) {
    long long j = (i + x) % n;
    for (auto u : V[i]) {
      long long k = (u + x) % n;
      G[j].push_back(k);
    }
  }
  for (long long i = 0; i < n; ++i) {
    sort((G[i]).begin(), (G[i]).end());
    if (V[i] != G[i]) {
      return 0;
    }
  }
  return 1;
}
int main() {
  localTest();
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> m;
  for (long long i = 1; i <= m; ++i) {
    long long x, y;
    cin >> x >> y;
    --x;
    --y;
    V[x].push_back(y);
    V[y].push_back(x);
  }
  for (long long i = 1; i * i <= n; ++i) {
    if (n % i == 0) {
      long long j = n / i;
      if (check(i) || check(j)) {
        cout << "YES\n";
        return 0;
      }
    }
  }
  cout << "NO\n";
  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;
vector<string> vec_splitter(string s) {
  for (char& c : s) c = c == ',' ? ' ' : c;
  stringstream ss;
  ss << s;
  vector<string> res;
  for (string z; ss >> z; res.push_back(z))
    ;
  return res;
}
void debug_out(vector<string> args, int idx) { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(vector<string> args, int idx, Head H, Tail... T) {
  if (idx > 0) cerr << ", ";
  stringstream ss;
  ss << H;
  cerr << args[idx] << " = " << ss.str();
  debug_out(args, idx + 1, T...);
}
void localTest() {}
const long long N = 1e5 + 5;
vector<long long> V[N], G[N];
long long n, m;
bool check(long long x) {
  if (x == n) {
    return 0;
  }
  for (long long i = 0; i < n; ++i) {
    G[i].clear();
    sort((V[i]).begin(), (V[i]).end());
  }
  for (long long i = 0; i < n; ++i) {
    long long j = (i + x) % n;
    for (auto u : V[i]) {
      long long k = (u + x) % n;
      G[j].push_back(k);
    }
  }
  for (long long i = 0; i < n; ++i) {
    sort((G[i]).begin(), (G[i]).end());
    if (V[i] != G[i]) {
      return 0;
    }
  }
  return 1;
}
int main() {
  localTest();
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> m;
  for (long long i = 1; i <= m; ++i) {
    long long x, y;
    cin >> x >> y;
    --x;
    --y;
    V[x].push_back(y);
    V[y].push_back(x);
  }
  for (long long i = 1; i * i <= n; ++i) {
    if (n % i == 0) {
      long long j = n / i;
      if (check(i) || check(j)) {
        cout << "YES\n";
        return 0;
      }
    }
  }
  cout << "NO\n";
  return 0;
}

```