#include <bits/stdc++.h>
using namespace std;
void print(long long int a[], long long int n) {
  for (long long int i = 0; i < n; i++) {
    cout << a[i] << " ";
  }
  cout << endl;
}
long long int m(long long int x) { return x % 1000000007; }
long long int gcd(long long int a, long long int b) {
  if (a == 0) return b;
  return gcd(b % a, a);
}
long long int p(long long int a, long long int b) {
  if (b == 0) return 1;
  long long int t = p(a, b / 2);
  if (b % 2 == 0)
    return t * t;
  else
    return a * t * t;
}
long long int spf[10000000] = {0};
void seive() {
  for (long long int i = 2; i < 100009; i += 2) spf[i] = 2;
  for (long long int i = 2; i < 100009; i++) {
    if (spf[i] != 0) {
      continue;
    }
    spf[i] = i;
    for (long long int j = i; j * i < 100009; j++) {
      if (spf[j * i] == 0) {
        spf[j * i] = i;
      }
    }
  }
}
vector<long long int> get_p(long long int x) {
  vector<long long int> v;
  if (x == 0 || x == 1) {
    return v;
  }
  while (x > 1) {
    v.push_back(spf[x]);
    long long int y = spf[x];
    while (x % y == 0) {
      x = x / y;
      if (x == 1) {
        break;
      }
    }
  }
  return v;
}
signed main() {
  seive();
  long long int n, m;
  cin >> n >> m;
  vector<long long int> vv;
  vv = get_p(n);
  vector<pair<long long int, long long int> > v;
  for (long long int i = 0; i < m; i++) {
    long long int x, y;
    cin >> x >> y;
    v.push_back({min(x, y), max(x, y)});
  }
  sort(v.begin(), v.end());
  long long int u = 0;
  for (long long int i = 0; i < vv.size(); i++) {
    long long int x = n / vv[i];
    vector<pair<long long int, long long int> > vi;
    long long int uu = 0;
    for (long long int j = 0; j < m; j++) {
      long long int y = (v[j].first - 1 + x) % n + 1;
      long long int z = (v[j].second - 1 + x) % n + 1;
      vi.push_back({min(y, z), max(y, z)});
    }
    sort(vi.begin(), vi.end());
    for (long long int j = 0; j < m; j++) {
      if (v[j].first != vi[j].first || v[j].second != vi[j].second) {
        uu = 1;
        ;
      }
    }
    if (uu == 0) {
      u = 1;
    }
  }
  if (u == 1) {
    cout << "Yes" << endl;
  } else {
    cout << "No" << endl;
  }
  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>
using namespace std;
void print(long long int a[], long long int n) {
  for (long long int i = 0; i < n; i++) {
    cout << a[i] << " ";
  }
  cout << endl;
}
long long int m(long long int x) { return x % 1000000007; }
long long int gcd(long long int a, long long int b) {
  if (a == 0) return b;
  return gcd(b % a, a);
}
long long int p(long long int a, long long int b) {
  if (b == 0) return 1;
  long long int t = p(a, b / 2);
  if (b % 2 == 0)
    return t * t;
  else
    return a * t * t;
}
long long int spf[10000000] = {0};
void seive() {
  for (long long int i = 2; i < 100009; i += 2) spf[i] = 2;
  for (long long int i = 2; i < 100009; i++) {
    if (spf[i] != 0) {
      continue;
    }
    spf[i] = i;
    for (long long int j = i; j * i < 100009; j++) {
      if (spf[j * i] == 0) {
        spf[j * i] = i;
      }
    }
  }
}
vector<long long int> get_p(long long int x) {
  vector<long long int> v;
  if (x == 0 || x == 1) {
    return v;
  }
  while (x > 1) {
    v.push_back(spf[x]);
    long long int y = spf[x];
    while (x % y == 0) {
      x = x / y;
      if (x == 1) {
        break;
      }
    }
  }
  return v;
}
signed main() {
  seive();
  long long int n, m;
  cin >> n >> m;
  vector<long long int> vv;
  vv = get_p(n);
  vector<pair<long long int, long long int> > v;
  for (long long int i = 0; i < m; i++) {
    long long int x, y;
    cin >> x >> y;
    v.push_back({min(x, y), max(x, y)});
  }
  sort(v.begin(), v.end());
  long long int u = 0;
  for (long long int i = 0; i < vv.size(); i++) {
    long long int x = n / vv[i];
    vector<pair<long long int, long long int> > vi;
    long long int uu = 0;
    for (long long int j = 0; j < m; j++) {
      long long int y = (v[j].first - 1 + x) % n + 1;
      long long int z = (v[j].second - 1 + x) % n + 1;
      vi.push_back({min(y, z), max(y, z)});
    }
    sort(vi.begin(), vi.end());
    for (long long int j = 0; j < m; j++) {
      if (v[j].first != vi[j].first || v[j].second != vi[j].second) {
        uu = 1;
        ;
      }
    }
    if (uu == 0) {
      u = 1;
    }
  }
  if (u == 1) {
    cout << "Yes" << endl;
  } else {
    cout << "No" << endl;
  }
  return 0;
}

```