#include <bits/stdc++.h>
using namespace std;
long double const pi = 3.141592653589793238462;
long long int const mod = 1e9 + 7;
long long int const mod1 = 1e9 + 6;
long long int power(long long int a, long long int b) {
  long long int f = 1;
  while (b > 0) {
    if (b & 1) {
      f = f * a;
      f %= mod;
    }
    a = a * a;
    a %= mod;
    b = b / 2;
  }
  return f;
}
long long int inverse_mod(long long int x) { return power(x, mod - 2); }
long long int const N = 2e5 + 5;
vector<long long int> v[N];
long long int lps[N];
long long int n, m;
bool isequal(long long int x, long long int y) {
  x = x % n;
  y = y % n;
  if (v[x].size() == v[y].size()) {
    for (long long int i = 0; i < v[x].size(); i++) {
      if (v[x][i] != v[y][i]) return false;
    }
    return true;
  } else {
    return false;
  }
}
void kmp() {
  lps[0] = 0;
  for (long long int i = 1; i < 2 * n; i++) {
    long long int j = lps[i - 1];
    while (j > 0 && !isequal(i, j)) {
      j = lps[j - 1];
    }
    if (isequal(i, j)) {
      lps[i] = j + 1;
    } else {
      lps[i] = j;
    }
  }
}
int32_t main() {
  std::ios::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  ;
  long long int i, j, l;
  cin >> n >> m;
  for (i = 0; i < m; i++) {
    long long int x, y;
    cin >> x >> y;
    x--;
    y--;
    if (y > x) {
      v[x].push_back(y - x);
      v[y].push_back(x + n - y);
    } else {
      v[x].push_back(y + n - x);
      v[y].push_back(x - y);
    }
  }
  for (i = 0; i < n; i++) {
    sort(v[i].begin(), v[i].end());
  }
  kmp();
  long long int is = 0;
  for (i = n; i < 2 * n - 1; i++) {
    if (lps[i] >= n) is = 1;
  }
  if (is) {
    cout << "Yes" << endl;
  } else {
    cout << "No" << endl;
  }
  return 0;
}

### Prompt

Generate 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;
long double const pi = 3.141592653589793238462;
long long int const mod = 1e9 + 7;
long long int const mod1 = 1e9 + 6;
long long int power(long long int a, long long int b) {
  long long int f = 1;
  while (b > 0) {
    if (b & 1) {
      f = f * a;
      f %= mod;
    }
    a = a * a;
    a %= mod;
    b = b / 2;
  }
  return f;
}
long long int inverse_mod(long long int x) { return power(x, mod - 2); }
long long int const N = 2e5 + 5;
vector<long long int> v[N];
long long int lps[N];
long long int n, m;
bool isequal(long long int x, long long int y) {
  x = x % n;
  y = y % n;
  if (v[x].size() == v[y].size()) {
    for (long long int i = 0; i < v[x].size(); i++) {
      if (v[x][i] != v[y][i]) return false;
    }
    return true;
  } else {
    return false;
  }
}
void kmp() {
  lps[0] = 0;
  for (long long int i = 1; i < 2 * n; i++) {
    long long int j = lps[i - 1];
    while (j > 0 && !isequal(i, j)) {
      j = lps[j - 1];
    }
    if (isequal(i, j)) {
      lps[i] = j + 1;
    } else {
      lps[i] = j;
    }
  }
}
int32_t main() {
  std::ios::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  ;
  long long int i, j, l;
  cin >> n >> m;
  for (i = 0; i < m; i++) {
    long long int x, y;
    cin >> x >> y;
    x--;
    y--;
    if (y > x) {
      v[x].push_back(y - x);
      v[y].push_back(x + n - y);
    } else {
      v[x].push_back(y + n - x);
      v[y].push_back(x - y);
    }
  }
  for (i = 0; i < n; i++) {
    sort(v[i].begin(), v[i].end());
  }
  kmp();
  long long int is = 0;
  for (i = n; i < 2 * n - 1; i++) {
    if (lps[i] >= n) is = 1;
  }
  if (is) {
    cout << "Yes" << endl;
  } else {
    cout << "No" << endl;
  }
  return 0;
}

```