#include <bits/stdc++.h>
using namespace std;
template <typename T>
void maxtt(T& t1, T t2) {
  t1 = max(t1, t2);
}
template <typename T>
void mintt(T& t1, T t2) {
  t1 = min(t1, t2);
}
bool debug = 0;
int n, m, k;
int dx[4] = {0, 1, 0, -1}, dy[4] = {1, 0, -1, 0};
string direc = "URDL";
long long ln, lk, lm;
void etp(bool f = 0) {
  puts(f ? "YES" : "NO");
  exit(0);
}
void addmod(int& x, int y, int mod = 998244353) {
  assert(y >= 0);
  x += y;
  if (x >= mod) x -= mod;
  assert(x >= 0 && x < mod);
}
void et(int x = -1) {
  printf("%d\n", x);
  exit(0);
}
long long fastPow(long long x, long long y, int mod = 998244353) {
  long long ans = 1;
  while (y > 0) {
    if (y & 1) ans = (x * ans) % mod;
    x = x * x % mod;
    y >>= 1;
  }
  return ans;
}
long long gcd1(long long x, long long y) { return y ? gcd1(y, x % y) : x; }
vector<int> sp[100035];
int a[100035 * 2], b[100035 * 2], N;
vector<int> vp;
int z[100035 * 10];
void zFunc(int n) {
  int L = 0, R = 0;
  for (int i = 1; i < n; i++) {
    if (i > R) {
      L = R = i;
      while (R < n && vp[R] == vp[R - L]) R++;
      R--;
      z[i] = R - L + 1;
    } else {
      int k = i - L;
      if (z[k] < R - i + 1)
        z[i] = z[k];
      else {
        L = i;
        while (R < n && vp[R] == vp[R - L]) R++;
        R--;
        z[i] = R - L + 1;
      }
    }
  }
}
void fmain(int tid) {
  scanf("%d%d", &n, &m);
  for (int(i) = 1; (i) <= (int)(m); (i)++) scanf("%d%d", a + i, b + i);
  for (int(i) = 1; (i) <= (int)(m); (i)++) {
    int len = b[i] - a[i];
    if (len < 0) len += n;
    sp[a[i]].push_back(len);
    len = a[i] - b[i];
    if (len < 0) len += n;
    sp[b[i]].push_back(len);
  }
  for (int(i) = 1; (i) <= (int)(n); (i)++) {
    sort(sp[i].begin(), sp[i].end());
    for (int z : sp[i]) vp.push_back(z);
    vp.push_back(-1);
  }
  N = vp.size();
  int nn = N + N;
  for (int(i) = 0; (i) < (int)(N); (i)++) vp.push_back(vp[i]);
  zFunc(nn);
  for (int i = 1; i < N; i++) {
    if (z[i] >= N) etp(1);
  }
  etp();
}
int main() {
  int t = 1;
  for (int(i) = 1; (i) <= (int)(t); (i)++) {
    fmain(i);
  }
  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;
template <typename T>
void maxtt(T& t1, T t2) {
  t1 = max(t1, t2);
}
template <typename T>
void mintt(T& t1, T t2) {
  t1 = min(t1, t2);
}
bool debug = 0;
int n, m, k;
int dx[4] = {0, 1, 0, -1}, dy[4] = {1, 0, -1, 0};
string direc = "URDL";
long long ln, lk, lm;
void etp(bool f = 0) {
  puts(f ? "YES" : "NO");
  exit(0);
}
void addmod(int& x, int y, int mod = 998244353) {
  assert(y >= 0);
  x += y;
  if (x >= mod) x -= mod;
  assert(x >= 0 && x < mod);
}
void et(int x = -1) {
  printf("%d\n", x);
  exit(0);
}
long long fastPow(long long x, long long y, int mod = 998244353) {
  long long ans = 1;
  while (y > 0) {
    if (y & 1) ans = (x * ans) % mod;
    x = x * x % mod;
    y >>= 1;
  }
  return ans;
}
long long gcd1(long long x, long long y) { return y ? gcd1(y, x % y) : x; }
vector<int> sp[100035];
int a[100035 * 2], b[100035 * 2], N;
vector<int> vp;
int z[100035 * 10];
void zFunc(int n) {
  int L = 0, R = 0;
  for (int i = 1; i < n; i++) {
    if (i > R) {
      L = R = i;
      while (R < n && vp[R] == vp[R - L]) R++;
      R--;
      z[i] = R - L + 1;
    } else {
      int k = i - L;
      if (z[k] < R - i + 1)
        z[i] = z[k];
      else {
        L = i;
        while (R < n && vp[R] == vp[R - L]) R++;
        R--;
        z[i] = R - L + 1;
      }
    }
  }
}
void fmain(int tid) {
  scanf("%d%d", &n, &m);
  for (int(i) = 1; (i) <= (int)(m); (i)++) scanf("%d%d", a + i, b + i);
  for (int(i) = 1; (i) <= (int)(m); (i)++) {
    int len = b[i] - a[i];
    if (len < 0) len += n;
    sp[a[i]].push_back(len);
    len = a[i] - b[i];
    if (len < 0) len += n;
    sp[b[i]].push_back(len);
  }
  for (int(i) = 1; (i) <= (int)(n); (i)++) {
    sort(sp[i].begin(), sp[i].end());
    for (int z : sp[i]) vp.push_back(z);
    vp.push_back(-1);
  }
  N = vp.size();
  int nn = N + N;
  for (int(i) = 0; (i) < (int)(N); (i)++) vp.push_back(vp[i]);
  zFunc(nn);
  for (int i = 1; i < N; i++) {
    if (z[i] >= N) etp(1);
  }
  etp();
}
int main() {
  int t = 1;
  for (int(i) = 1; (i) <= (int)(t); (i)++) {
    fmain(i);
  }
  return 0;
}

```