#include <bits/stdc++.h>
using namespace std;
const int N = 1e5 + 5;
namespace KMP {
void get_nextval(const vector<int> &s, vector<int> &nxt) {
  int len = s.size();
  int i = 0;
  int k = -1;
  nxt[0] = -1;
  while (i < len) {
    if (k == -1 || s[k] == s[i]) {
      ++i;
      ++k;
      if (i == len || s[k] != s[i]) {
        nxt[i] = k;
      } else
        nxt[i] = nxt[k];
    } else
      k = nxt[k];
  }
}
int kmp(vector<int> &s1, vector<int> &s2) {
  int l1 = s1.size();
  int l2 = s2.size();
  vector<int> nxt(l2 + 1);
  get_nextval(s2, nxt);
  int i = 0, j = 0;
  int pre = -1;
  while (i < l1) {
    if (j == -1 || s1[i] == s2[j]) {
      ++i;
      ++j;
    } else
      j = nxt[j];
    if (j == l2) {
      if (pre == -1) {
        pre = i - l2;
        j = nxt[j];
      } else {
        return i - l2 - pre;
      }
    }
  }
  return -1;
}
}  // namespace KMP
long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); }
void fail() {
  puts("No");
  exit(0);
}
vector<int> dis[N];
int main() {
  int n, m;
  scanf("%d%d", &n, &m);
  for (int i = 0; i < m; ++i) {
    int x, y;
    scanf("%d%d", &x, &y);
    if (x > y) swap(x, y);
    int d = y - x;
    if (d > n / 2) {
      d = n - d;
      swap(x, y);
    }
    dis[d].push_back(x - 1);
  }
  long long lcm = 1;
  for (int i = 1; i <= n; ++i) {
    int len = dis[i].size();
    if (len) {
      if (2 * i == n) {
        lcm = lcm / gcd(lcm, 1ll * i) * i;
      } else if (len == 1) {
        fail();
      } else {
        sort(dis[i].begin(), dis[i].end());
        vector<int> s1(2 * len);
        vector<int> s2(len);
        for (int j = 0; j < 2 * len; ++j) {
          if (j < len) {
            s1[j] = s2[j] = (j == len - 1 ? n + dis[i][0] - dis[i][len - 1]
                                          : dis[i][j + 1] - dis[i][j]);
          } else {
            s1[j] = s1[j - len];
          }
        }
        int k = KMP::kmp(s1, s2);
        int step = 0;
        for (int j = 0; j < k; ++j) {
          step += s1[j];
        }
        lcm = lcm / gcd(lcm, 1ll * step) * step;
      }
      if (lcm >= n) {
        fail();
      }
    }
  }
  puts("Yes");
  return 0;
}

### Prompt

Please create a solution in Cpp 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;
const int N = 1e5 + 5;
namespace KMP {
void get_nextval(const vector<int> &s, vector<int> &nxt) {
  int len = s.size();
  int i = 0;
  int k = -1;
  nxt[0] = -1;
  while (i < len) {
    if (k == -1 || s[k] == s[i]) {
      ++i;
      ++k;
      if (i == len || s[k] != s[i]) {
        nxt[i] = k;
      } else
        nxt[i] = nxt[k];
    } else
      k = nxt[k];
  }
}
int kmp(vector<int> &s1, vector<int> &s2) {
  int l1 = s1.size();
  int l2 = s2.size();
  vector<int> nxt(l2 + 1);
  get_nextval(s2, nxt);
  int i = 0, j = 0;
  int pre = -1;
  while (i < l1) {
    if (j == -1 || s1[i] == s2[j]) {
      ++i;
      ++j;
    } else
      j = nxt[j];
    if (j == l2) {
      if (pre == -1) {
        pre = i - l2;
        j = nxt[j];
      } else {
        return i - l2 - pre;
      }
    }
  }
  return -1;
}
}  // namespace KMP
long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); }
void fail() {
  puts("No");
  exit(0);
}
vector<int> dis[N];
int main() {
  int n, m;
  scanf("%d%d", &n, &m);
  for (int i = 0; i < m; ++i) {
    int x, y;
    scanf("%d%d", &x, &y);
    if (x > y) swap(x, y);
    int d = y - x;
    if (d > n / 2) {
      d = n - d;
      swap(x, y);
    }
    dis[d].push_back(x - 1);
  }
  long long lcm = 1;
  for (int i = 1; i <= n; ++i) {
    int len = dis[i].size();
    if (len) {
      if (2 * i == n) {
        lcm = lcm / gcd(lcm, 1ll * i) * i;
      } else if (len == 1) {
        fail();
      } else {
        sort(dis[i].begin(), dis[i].end());
        vector<int> s1(2 * len);
        vector<int> s2(len);
        for (int j = 0; j < 2 * len; ++j) {
          if (j < len) {
            s1[j] = s2[j] = (j == len - 1 ? n + dis[i][0] - dis[i][len - 1]
                                          : dis[i][j + 1] - dis[i][j]);
          } else {
            s1[j] = s1[j - len];
          }
        }
        int k = KMP::kmp(s1, s2);
        int step = 0;
        for (int j = 0; j < k; ++j) {
          step += s1[j];
        }
        lcm = lcm / gcd(lcm, 1ll * step) * step;
      }
      if (lcm >= n) {
        fail();
      }
    }
  }
  puts("Yes");
  return 0;
}

```