#include <bits/stdc++.h>
const long long inf = 0x3f3f3f3f3f3f3f3LL;
const long long mod = (long long)1e9 + 7;
using namespace std;
template <class T, class T2>
void smin(T& a, T2 val) {
  if (a > val) a = val;
}
template <class T, class T2>
void smax(T& a, T2 val) {
  if (a < val) a = val;
}
const long long N = 5 * (long long)1e5 + 10;
long long n, m;
vector<long long> B[N];
vector<long long> A;
vector<long long> z_function(vector<long long>& s, long long n) {
  vector<long long> z(n);
  for (long long i = 1, l = 0, r = 0; i < n; ++i) {
    if (i <= r) {
      z[i] = min(r - i + 1, z[i - l]);
    }
    while (i + z[i] < n && s[z[i]] == s[i + z[i]]) {
      ++z[i];
    }
    if (i + z[i] - 1 > r) {
      l = i, r = i + z[i] - 1;
    }
  }
  return z;
}
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  cin >> n >> m;
  for (long long i = 0; i < m; ++i) {
    long long x, y;
    cin >> x >> y;
    if (x > y) {
      swap(x, y);
    }
    long long dist1 = y - x;
    B[x].push_back(dist1);
    long long dist2 = n - y + x;
    B[y].push_back(dist2);
  }
  for (long long i = 1; i <= n; ++i) {
    A.push_back(-1);
    sort(B[i].begin(), B[i].end());
    for (auto& it : B[i]) {
      A.push_back(it);
    }
  };
  long long len = (long long)(A.size());
  vector<long long> v = A;
  for (auto it : v) {
    A.push_back(it);
  }
  vector<long long> z = z_function(A, (long long)(A.size()));
  ;
  ;
  for (long long i = 1; i < len; ++i) {
    if (z[i] >= len) {
      cout << "Yes";
      exit(0);
    }
  }
  cout << "No";
  return 0;
}

### Prompt

Your challenge is to write 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>
const long long inf = 0x3f3f3f3f3f3f3f3LL;
const long long mod = (long long)1e9 + 7;
using namespace std;
template <class T, class T2>
void smin(T& a, T2 val) {
  if (a > val) a = val;
}
template <class T, class T2>
void smax(T& a, T2 val) {
  if (a < val) a = val;
}
const long long N = 5 * (long long)1e5 + 10;
long long n, m;
vector<long long> B[N];
vector<long long> A;
vector<long long> z_function(vector<long long>& s, long long n) {
  vector<long long> z(n);
  for (long long i = 1, l = 0, r = 0; i < n; ++i) {
    if (i <= r) {
      z[i] = min(r - i + 1, z[i - l]);
    }
    while (i + z[i] < n && s[z[i]] == s[i + z[i]]) {
      ++z[i];
    }
    if (i + z[i] - 1 > r) {
      l = i, r = i + z[i] - 1;
    }
  }
  return z;
}
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  cin >> n >> m;
  for (long long i = 0; i < m; ++i) {
    long long x, y;
    cin >> x >> y;
    if (x > y) {
      swap(x, y);
    }
    long long dist1 = y - x;
    B[x].push_back(dist1);
    long long dist2 = n - y + x;
    B[y].push_back(dist2);
  }
  for (long long i = 1; i <= n; ++i) {
    A.push_back(-1);
    sort(B[i].begin(), B[i].end());
    for (auto& it : B[i]) {
      A.push_back(it);
    }
  };
  long long len = (long long)(A.size());
  vector<long long> v = A;
  for (auto it : v) {
    A.push_back(it);
  }
  vector<long long> z = z_function(A, (long long)(A.size()));
  ;
  ;
  for (long long i = 1; i < len; ++i) {
    if (z[i] >= len) {
      cout << "Yes";
      exit(0);
    }
  }
  cout << "No";
  return 0;
}

```