#include <bits/stdc++.h>
using namespace std;
const long long mod = 1e9 + 7;
const long long INF = 4e18 + 10;
long long power(long long a, long long b, long long in_mod) {
  long long ans = 1;
  long long prod = a;
  while (b) {
    if (b % 2) ans = (ans * prod) % in_mod;
    prod = (prod * prod) % in_mod;
    b /= 2;
  }
  return ans;
}
long long mod_inv(long long q, long long in_mod) {
  return power(q, in_mod - 2, in_mod);
}
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long fact(long long n, long long in_mod) {
  long long f = 1;
  for (long long i = 1; i <= n; i++) f = (f * i) % in_mod;
  return f;
}
long long ncr(long long n, long long r, long long in_mod) {
  return (((fact(n, in_mod) * mod_inv(fact(r, in_mod), in_mod)) % in_mod) *
          mod_inv(fact(n - r, in_mod), in_mod)) %
         in_mod;
}
vector<long long> Z;
long long len;
long long prefix_function() {
  long long n = (long long)Z.size();
  vector<long long> F(n);
  F[0] = 0;
  for (long long i = 1; i < n; ++i) {
    long long j = F[i - 1];
    while (j > 0 && Z[i] != Z[j]) j = F[j - 1];
    if (Z[i] == Z[j]) ++j;
    F[i] = j;
  }
  for (long long i = 1; i < n - 1; i++) {
    if (F[i] == len) return 1;
  }
  return 0;
}
void solve() {
  long long n, m;
  cin >> n >> m;
  set<long long> s[n + 1];
  for (long long i = 1; i <= m; i++) {
    long long u, v;
    cin >> u >> v;
    s[u].insert((n + v - u) % n);
    s[v].insert((n + u - v) % n);
  }
  vector<long long> t;
  for (long long i = 1; i <= n; i++) {
    t.push_back(0);
    for (auto u : s[i]) {
      t.push_back(u);
    }
  }
  len = t.size();
  for (long long i = 0; i < t.size(); i++) Z.push_back(t[i]);
  for (long long i = 0; i < t.size(); i++) Z.push_back(t[i]);
  long long flag = prefix_function();
  if (flag)
    cout << "Yes" << '\n';
  else
    cout << "No" << '\n';
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  cout << fixed << setprecision(10);
  auto clk = clock();
  mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
  long long t = 1;
  for (long long test = 1; test <= t; test++) {
    solve();
  }
  clk = clock() - clk;
  cerr << fixed << setprecision(6)
       << "Time: " << ((long double)clk) / CLOCKS_PER_SEC << "\n";
  return 0;
}

### Prompt

In CPP, your task is to solve 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 long long mod = 1e9 + 7;
const long long INF = 4e18 + 10;
long long power(long long a, long long b, long long in_mod) {
  long long ans = 1;
  long long prod = a;
  while (b) {
    if (b % 2) ans = (ans * prod) % in_mod;
    prod = (prod * prod) % in_mod;
    b /= 2;
  }
  return ans;
}
long long mod_inv(long long q, long long in_mod) {
  return power(q, in_mod - 2, in_mod);
}
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long fact(long long n, long long in_mod) {
  long long f = 1;
  for (long long i = 1; i <= n; i++) f = (f * i) % in_mod;
  return f;
}
long long ncr(long long n, long long r, long long in_mod) {
  return (((fact(n, in_mod) * mod_inv(fact(r, in_mod), in_mod)) % in_mod) *
          mod_inv(fact(n - r, in_mod), in_mod)) %
         in_mod;
}
vector<long long> Z;
long long len;
long long prefix_function() {
  long long n = (long long)Z.size();
  vector<long long> F(n);
  F[0] = 0;
  for (long long i = 1; i < n; ++i) {
    long long j = F[i - 1];
    while (j > 0 && Z[i] != Z[j]) j = F[j - 1];
    if (Z[i] == Z[j]) ++j;
    F[i] = j;
  }
  for (long long i = 1; i < n - 1; i++) {
    if (F[i] == len) return 1;
  }
  return 0;
}
void solve() {
  long long n, m;
  cin >> n >> m;
  set<long long> s[n + 1];
  for (long long i = 1; i <= m; i++) {
    long long u, v;
    cin >> u >> v;
    s[u].insert((n + v - u) % n);
    s[v].insert((n + u - v) % n);
  }
  vector<long long> t;
  for (long long i = 1; i <= n; i++) {
    t.push_back(0);
    for (auto u : s[i]) {
      t.push_back(u);
    }
  }
  len = t.size();
  for (long long i = 0; i < t.size(); i++) Z.push_back(t[i]);
  for (long long i = 0; i < t.size(); i++) Z.push_back(t[i]);
  long long flag = prefix_function();
  if (flag)
    cout << "Yes" << '\n';
  else
    cout << "No" << '\n';
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  cout << fixed << setprecision(10);
  auto clk = clock();
  mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
  long long t = 1;
  for (long long test = 1; test <= t; test++) {
    solve();
  }
  clk = clock() - clk;
  cerr << fixed << setprecision(6)
       << "Time: " << ((long double)clk) / CLOCKS_PER_SEC << "\n";
  return 0;
}

```