#include <bits/stdc++.h>
using namespace std;
const int N = 1e5 + 10;
set<int> f[N];
bool tf1 = true;
inline int read() {
  int x = 0, k = 1;
  char c = getchar();
  for (; c < 48 || c > 57; c = getchar()) k ^= (c == '-');
  for (; c >= 48 && c <= 57; c = getchar()) x = x * 10 + (c ^ 48);
  return k ? x : -x;
}
int main() {
  int n = read(), m = read(), a, b;
  while (m--) a = read(), b = read(), f[--a].insert(--b), f[b].insert(a);
  for (int i = 1; i < n; i++)
    if (!(n % i)) {
      tf1 = true;
      for (int x = 0; x < n; x++)
        for (auto y : f[x]) tf1 &= f[(x + i) % n].count((y + i) % n);
      if (tf1) return printf("Yes\n"), 0;
    }
  printf("No\n");
  return 0;
}

### Prompt

Please create a solution in CPP 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 int N = 1e5 + 10;
set<int> f[N];
bool tf1 = true;
inline int read() {
  int x = 0, k = 1;
  char c = getchar();
  for (; c < 48 || c > 57; c = getchar()) k ^= (c == '-');
  for (; c >= 48 && c <= 57; c = getchar()) x = x * 10 + (c ^ 48);
  return k ? x : -x;
}
int main() {
  int n = read(), m = read(), a, b;
  while (m--) a = read(), b = read(), f[--a].insert(--b), f[b].insert(a);
  for (int i = 1; i < n; i++)
    if (!(n % i)) {
      tf1 = true;
      for (int x = 0; x < n; x++)
        for (auto y : f[x]) tf1 &= f[(x + i) % n].count((y + i) % n);
      if (tf1) return printf("Yes\n"), 0;
    }
  printf("No\n");
  return 0;
}

```