#include <bits/stdc++.h>
using namespace std;
inline long long gcd(long long x, long long y) { return x ? gcd(y % x, x) : y; }
const long long mod = 1e9 + 7;
inline long long QPow(long long a, long long b) {
  long long ans = 1;
  while (b) {
    if (b & 1) ans = ans * a % mod;
    a = a * a % mod;
    b >>= 1;
  }
  return ans;
}
const long long maxn = 5e5 + 5;
vector<long long> divisor;
vector<long long> prim_divisor;
bool vis[maxn];
long long prim[maxn];
long long top = 0;
void init() {
  top = 0;
  vis[0] = vis[1] = 1;
  for (long long i = 2; i < maxn; i++) {
    if (!vis[i]) prim[top++] = i;
    for (long long j = 0; j < top && (long long)i * prim[j] < maxn; j++) {
      vis[i * prim[j]] = 1;
      if (i % prim[j] == 0) break;
    }
  }
}
long long exgcd(long long a, long long b, long long &x, long long &y) {
  long long d = a;
  if (b == 0)
    x = 1, y = 0;
  else {
    d = exgcd(b, a % b, y, x), y -= a / b * x;
  }
  return d;
}
vector<signed> g[maxn];
vector<signed> tmp[maxn];
long long n;
signed vis1[maxn];
signed vis2[maxn];
bool check(long long x) {
  for (long long i = 0; i <= n; i++) tmp[i].clear();
  for (long long i = 1; i <= n; i++) {
    for (long long j = 0; j < g[i].size(); j++) {
      long long u = i, v = g[i][j];
      u += x, v += x;
      if (u > n) u = u - n;
      if (v > n) v -= n;
      if (u > v) swap(u, v);
      tmp[u].push_back(v);
    }
  }
  bool flag = 1;
  for (long long i = 1; i <= n && flag; i++) {
    if (tmp[i].size() != g[i].size()) {
      flag = 0;
      return flag;
    }
    for (long long j = 0; j < tmp[i].size(); j++) vis1[tmp[i][j]] += 1;
    for (long long j = 0; j < g[i].size(); j++) vis2[g[i][j]] += 1;
    for (long long j = 0; j < tmp[i].size(); j++) {
      if (vis1[tmp[i][j]] != vis2[tmp[i][j]]) flag = 0;
    }
    for (long long j = 0; j < tmp[i].size(); j++)
      vis1[tmp[i][j]] = 0, vis2[g[i][j]] = 0;
  }
  return flag;
}
signed main() {
  ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  long long t, m, q;
  cin >> n >> m;
  for (long long i = 1; i <= m; i++) {
    signed u, v;
    cin >> u >> v;
    if (u > v) swap(u, v);
    g[u].push_back(v);
  }
  long long sq = sqrt(n);
  bool ans = 0;
  for (long long i = 1; i <= sq; i++) {
    if (n % i == 0) {
      ans |= check(i);
      if (i != 1) ans |= check(n / i);
    }
  }
  if (ans)
    cout << "Yes\n";
  else
    cout << "No\n";
  return 0;
}

### Prompt

Your task is to create 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;
inline long long gcd(long long x, long long y) { return x ? gcd(y % x, x) : y; }
const long long mod = 1e9 + 7;
inline long long QPow(long long a, long long b) {
  long long ans = 1;
  while (b) {
    if (b & 1) ans = ans * a % mod;
    a = a * a % mod;
    b >>= 1;
  }
  return ans;
}
const long long maxn = 5e5 + 5;
vector<long long> divisor;
vector<long long> prim_divisor;
bool vis[maxn];
long long prim[maxn];
long long top = 0;
void init() {
  top = 0;
  vis[0] = vis[1] = 1;
  for (long long i = 2; i < maxn; i++) {
    if (!vis[i]) prim[top++] = i;
    for (long long j = 0; j < top && (long long)i * prim[j] < maxn; j++) {
      vis[i * prim[j]] = 1;
      if (i % prim[j] == 0) break;
    }
  }
}
long long exgcd(long long a, long long b, long long &x, long long &y) {
  long long d = a;
  if (b == 0)
    x = 1, y = 0;
  else {
    d = exgcd(b, a % b, y, x), y -= a / b * x;
  }
  return d;
}
vector<signed> g[maxn];
vector<signed> tmp[maxn];
long long n;
signed vis1[maxn];
signed vis2[maxn];
bool check(long long x) {
  for (long long i = 0; i <= n; i++) tmp[i].clear();
  for (long long i = 1; i <= n; i++) {
    for (long long j = 0; j < g[i].size(); j++) {
      long long u = i, v = g[i][j];
      u += x, v += x;
      if (u > n) u = u - n;
      if (v > n) v -= n;
      if (u > v) swap(u, v);
      tmp[u].push_back(v);
    }
  }
  bool flag = 1;
  for (long long i = 1; i <= n && flag; i++) {
    if (tmp[i].size() != g[i].size()) {
      flag = 0;
      return flag;
    }
    for (long long j = 0; j < tmp[i].size(); j++) vis1[tmp[i][j]] += 1;
    for (long long j = 0; j < g[i].size(); j++) vis2[g[i][j]] += 1;
    for (long long j = 0; j < tmp[i].size(); j++) {
      if (vis1[tmp[i][j]] != vis2[tmp[i][j]]) flag = 0;
    }
    for (long long j = 0; j < tmp[i].size(); j++)
      vis1[tmp[i][j]] = 0, vis2[g[i][j]] = 0;
  }
  return flag;
}
signed main() {
  ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  long long t, m, q;
  cin >> n >> m;
  for (long long i = 1; i <= m; i++) {
    signed u, v;
    cin >> u >> v;
    if (u > v) swap(u, v);
    g[u].push_back(v);
  }
  long long sq = sqrt(n);
  bool ans = 0;
  for (long long i = 1; i <= sq; i++) {
    if (n % i == 0) {
      ans |= check(i);
      if (i != 1) ans |= check(n / i);
    }
  }
  if (ans)
    cout << "Yes\n";
  else
    cout << "No\n";
  return 0;
}

```