#include <bits/stdc++.h>
using namespace std;
const long long int maxn = 1e5;
vector<pair<int, int>> arr;
unordered_map<int, unordered_map<int, int>> m;
long long int n, k;
bool check(int k) {
  for (auto &i : arr) {
    int a = i.first + k;
    int b = i.second + k;
    if (a > n) a -= n;
    if (b > n) b -= n;
    bool p = false;
    if (m.find(a) != m.end() && m[a].find(b) != m[a].end()) p = true;
    if (m.find(b) != m.end() && m[b].find(a) != m[b].end()) p = true;
    if (!p) return false;
  }
  return true;
}
int main() {
  cin >> n >> k;
  for (int i = 0; i < k; i++) {
    int a, b;
    cin >> a >> b;
    arr.push_back(make_pair(a, b));
    m[a][b]++;
    m[b][a]++;
  }
  for (int i = 1; i * i <= n; ++i) {
    if (n % i != 0) continue;
    int d1 = n / i;
    int d2 = i;
    if (d1 != n && check(d1)) {
      cout << "Yes\n";
      return 0;
    }
    if (d2 != n && check(d2)) {
      cout << "Yes\n";
      return 0;
    }
  }
  cout << "No\n";
  return 0;
}

### Prompt

Please formulate 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;
const long long int maxn = 1e5;
vector<pair<int, int>> arr;
unordered_map<int, unordered_map<int, int>> m;
long long int n, k;
bool check(int k) {
  for (auto &i : arr) {
    int a = i.first + k;
    int b = i.second + k;
    if (a > n) a -= n;
    if (b > n) b -= n;
    bool p = false;
    if (m.find(a) != m.end() && m[a].find(b) != m[a].end()) p = true;
    if (m.find(b) != m.end() && m[b].find(a) != m[b].end()) p = true;
    if (!p) return false;
  }
  return true;
}
int main() {
  cin >> n >> k;
  for (int i = 0; i < k; i++) {
    int a, b;
    cin >> a >> b;
    arr.push_back(make_pair(a, b));
    m[a][b]++;
    m[b][a]++;
  }
  for (int i = 1; i * i <= n; ++i) {
    if (n % i != 0) continue;
    int d1 = n / i;
    int d2 = i;
    if (d1 != n && check(d1)) {
      cout << "Yes\n";
      return 0;
    }
    if (d2 != n && check(d2)) {
      cout << "Yes\n";
      return 0;
    }
  }
  cout << "No\n";
  return 0;
}

```