#include <bits/stdc++.h>
using namespace std;
int n, m;
vector<vector<int>> edges;
string answer;
void ReadInput() {
  cin >> n >> m;
  edges.resize(n + 1);
  int start, finish;
  for (size_t i = 0; i < m; i++) {
    cin >> start >> finish;
    edges[start].push_back(finish);
    edges[finish].push_back(start);
  }
}
void getZarr(string str, int Z[]);
bool search(string text, string pattern) {
  string concat = pattern + "$" + text;
  int l = concat.length();
  int Z[l];
  getZarr(concat, Z);
  for (int i = 0; i < l; ++i) {
    if (Z[i] == pattern.length()) return true;
  }
  return false;
}
void getZarr(string str, int Z[]) {
  int n = str.length();
  int L, R, k;
  L = R = 0;
  for (int i = 1; i < n; ++i) {
    if (i > R) {
      L = R = i;
      while (R < n && str[R - L] == str[R]) R++;
      Z[i] = R - L;
      R--;
    } else {
      k = i - L;
      if (Z[k] < R - i + 1)
        Z[i] = Z[k];
      else {
        L = i;
        while (R < n && str[R - L] == str[R]) R++;
        Z[i] = R - L;
        R--;
      }
    }
  }
}
string Solve() {
  for (size_t i = 1; i <= n; i++)
    for (size_t j = 0; j < edges[i].size(); j++)
      edges[i][j] = (edges[i][j] - i + n) % n;
  for (size_t i = 1; i <= n; i++) sort(edges[i].begin(), edges[i].end());
  string pattern;
  string text;
  for (size_t i = 1; i <= n; i++) {
    pattern += to_string(edges[i].size());
    pattern += ':';
    for (size_t j = 0; j < edges[i].size(); j++) {
      pattern += to_string(edges[i][j]);
      pattern += '#';
    }
    pattern += '!';
  }
  text = pattern + pattern;
  text.pop_back();
  text = text.substr(text.find("!") + 1);
  edges.clear();
  if (search(text, pattern)) return "Yes";
  return "No";
}
void WriteOutput() { cout << answer << endl; }
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  ReadInput();
  answer = Solve();
  WriteOutput();
  return 0;
}

### Prompt

Your task is to create a CPP solution to 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;
int n, m;
vector<vector<int>> edges;
string answer;
void ReadInput() {
  cin >> n >> m;
  edges.resize(n + 1);
  int start, finish;
  for (size_t i = 0; i < m; i++) {
    cin >> start >> finish;
    edges[start].push_back(finish);
    edges[finish].push_back(start);
  }
}
void getZarr(string str, int Z[]);
bool search(string text, string pattern) {
  string concat = pattern + "$" + text;
  int l = concat.length();
  int Z[l];
  getZarr(concat, Z);
  for (int i = 0; i < l; ++i) {
    if (Z[i] == pattern.length()) return true;
  }
  return false;
}
void getZarr(string str, int Z[]) {
  int n = str.length();
  int L, R, k;
  L = R = 0;
  for (int i = 1; i < n; ++i) {
    if (i > R) {
      L = R = i;
      while (R < n && str[R - L] == str[R]) R++;
      Z[i] = R - L;
      R--;
    } else {
      k = i - L;
      if (Z[k] < R - i + 1)
        Z[i] = Z[k];
      else {
        L = i;
        while (R < n && str[R - L] == str[R]) R++;
        Z[i] = R - L;
        R--;
      }
    }
  }
}
string Solve() {
  for (size_t i = 1; i <= n; i++)
    for (size_t j = 0; j < edges[i].size(); j++)
      edges[i][j] = (edges[i][j] - i + n) % n;
  for (size_t i = 1; i <= n; i++) sort(edges[i].begin(), edges[i].end());
  string pattern;
  string text;
  for (size_t i = 1; i <= n; i++) {
    pattern += to_string(edges[i].size());
    pattern += ':';
    for (size_t j = 0; j < edges[i].size(); j++) {
      pattern += to_string(edges[i][j]);
      pattern += '#';
    }
    pattern += '!';
  }
  text = pattern + pattern;
  text.pop_back();
  text = text.substr(text.find("!") + 1);
  edges.clear();
  if (search(text, pattern)) return "Yes";
  return "No";
}
void WriteOutput() { cout << answer << endl; }
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  ReadInput();
  answer = Solve();
  WriteOutput();
  return 0;
}

```