#include <bits/stdc++.h>
using namespace std;
int n, m;
set<pair<int, int>> s;
bool check(int x) {
  for (const auto& [u, v] : s)
    if (s.find(make_pair(((u - 1 + x) % n) + 1, ((v - 1 + x) % n) + 1)) ==
        s.end())
      return false;
  return true;
}
int main() {
  scanf("%d %d", &n, &m);
  for (int i = 1, u, v; i <= m; ++i)
    scanf("%d %d", &u, &v), s.insert(make_pair(u, v)),
        s.insert(make_pair(v, u));
  for (int i = 1; i < n; ++i)
    if (n % i == 0 && check(i)) printf("Yes\n"), exit(0);
  printf("No\n");
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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;
set<pair<int, int>> s;
bool check(int x) {
  for (const auto& [u, v] : s)
    if (s.find(make_pair(((u - 1 + x) % n) + 1, ((v - 1 + x) % n) + 1)) ==
        s.end())
      return false;
  return true;
}
int main() {
  scanf("%d %d", &n, &m);
  for (int i = 1, u, v; i <= m; ++i)
    scanf("%d %d", &u, &v), s.insert(make_pair(u, v)),
        s.insert(make_pair(v, u));
  for (int i = 1; i < n; ++i)
    if (n % i == 0 && check(i)) printf("Yes\n"), exit(0);
  printf("No\n");
}

```