#include <bits/stdc++.h>
#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target( \
    "sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,tune=native")
using namespace std;
void itval(istream_iterator<string> it) {}
template <typename T, typename... Args>
void itval(istream_iterator<string> it, T a, Args... args) {
  cerr << *it << " = " << a << endl;
  itval(++it, args...);
}
const long long int MOD = 1e9 + 7;
template <typename T>
inline void print(T x) {
  cout << x << "\n";
}
template <typename T>
inline void printvec(T x) {
  for (auto a : x) cout << a << ' ';
  cout << '\n';
}
struct custom {
  bool operator()(
      const pair<pair<long long int, long long int>, long long int> &p1,
      const pair<pair<long long int, long long int>, long long int> &p2) const {
    return p1.second > p2.second;
  }
};
long long int get_pow(long long int a, long long int b) {
  long long int res = 1;
  while (b) {
    if (b & 1) res = (res * a) % MOD;
    a = (a * a) % MOD;
    b >>= 1;
  }
  return res;
}
const long long int N = 1e5 + 5, inf = 1e18;
int n, m;
std::vector<pair<long long int, long long int> > v;
map<pair<long long int, long long int>, bool> mp;
bool calc(int j) {
  for (auto p : v) {
    long long int x = (p.first + j) % n, y = (p.second + j) % n;
    if (x < y) {
      if (!mp.count(make_pair(x, y))) {
        return 0;
      }
    } else {
      if (!mp.count(make_pair(y, x))) {
        return 0;
      }
    }
  }
  return 1;
}
void solve() {
  cin >> n >> m;
  v.resize(m);
  for (long long int i = (long long int)0; i < (long long int)(m); i++) {
    cin >> v[i].first >> v[i].second;
    v[i].first--;
    v[i].second--;
    if (v[i].second < v[i].first) swap(v[i].first, v[i].second);
    mp[v[i]] = 1;
  }
  if (calc(1)) {
    cout << "Yes\n";
    return;
  }
  for (long long int i = (long long int)2; i < (long long int)(sqrt(n) + 1);
       i++) {
    if (n % i == 0) {
      if (calc(i)) {
        cout << "Yes\n";
        return;
      }
      if (i * i != n && calc(n / i)) {
        cout << "Yes\n";
        return;
      }
    }
  }
  cout << "No\n";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int test = 1;
  clock_t z = clock();
  for (long long int tes = (long long int)0; tes < (long long int)(test);
       tes++) {
    solve();
  }
  fprintf(stderr, "Total Time:%.4f\n", (double)(clock() - z) / CLOCKS_PER_SEC),
      fflush(stderr);
  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>
#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target( \
    "sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,tune=native")
using namespace std;
void itval(istream_iterator<string> it) {}
template <typename T, typename... Args>
void itval(istream_iterator<string> it, T a, Args... args) {
  cerr << *it << " = " << a << endl;
  itval(++it, args...);
}
const long long int MOD = 1e9 + 7;
template <typename T>
inline void print(T x) {
  cout << x << "\n";
}
template <typename T>
inline void printvec(T x) {
  for (auto a : x) cout << a << ' ';
  cout << '\n';
}
struct custom {
  bool operator()(
      const pair<pair<long long int, long long int>, long long int> &p1,
      const pair<pair<long long int, long long int>, long long int> &p2) const {
    return p1.second > p2.second;
  }
};
long long int get_pow(long long int a, long long int b) {
  long long int res = 1;
  while (b) {
    if (b & 1) res = (res * a) % MOD;
    a = (a * a) % MOD;
    b >>= 1;
  }
  return res;
}
const long long int N = 1e5 + 5, inf = 1e18;
int n, m;
std::vector<pair<long long int, long long int> > v;
map<pair<long long int, long long int>, bool> mp;
bool calc(int j) {
  for (auto p : v) {
    long long int x = (p.first + j) % n, y = (p.second + j) % n;
    if (x < y) {
      if (!mp.count(make_pair(x, y))) {
        return 0;
      }
    } else {
      if (!mp.count(make_pair(y, x))) {
        return 0;
      }
    }
  }
  return 1;
}
void solve() {
  cin >> n >> m;
  v.resize(m);
  for (long long int i = (long long int)0; i < (long long int)(m); i++) {
    cin >> v[i].first >> v[i].second;
    v[i].first--;
    v[i].second--;
    if (v[i].second < v[i].first) swap(v[i].first, v[i].second);
    mp[v[i]] = 1;
  }
  if (calc(1)) {
    cout << "Yes\n";
    return;
  }
  for (long long int i = (long long int)2; i < (long long int)(sqrt(n) + 1);
       i++) {
    if (n % i == 0) {
      if (calc(i)) {
        cout << "Yes\n";
        return;
      }
      if (i * i != n && calc(n / i)) {
        cout << "Yes\n";
        return;
      }
    }
  }
  cout << "No\n";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int test = 1;
  clock_t z = clock();
  for (long long int tes = (long long int)0; tes < (long long int)(test);
       tes++) {
    solve();
  }
  fprintf(stderr, "Total Time:%.4f\n", (double)(clock() - z) / CLOCKS_PER_SEC),
      fflush(stderr);
  return 0;
}

```