#include <bits/stdc++.h>
struct Segment {
  int l, r;
};
Segment a[200005];
int seq[400005];
int s[1200005];
int next[1200005];
int vis[100005];
int good[100005];
int pos[100005];
void kmp(int n) {
  next[1] = 0;
  for (int i = 2; i <= n; i++) {
    int j = next[i - 1];
    while (j != 0 && s[j + 1] != s[i]) j = next[j];
    if (s[j + 1] == s[i]) j++;
    next[i] = j;
  }
}
int isSelfMatch(int n) {
  int size = 0;
  for (int i = 1; i <= n; i++) s[++size] = seq[i];
  s[++size] = 1e9 + 7;
  for (int i = 1; i <= n; i++) s[++size] = seq[i];
  for (int i = 1; i <= n; i++) s[++size] = seq[i];
  kmp(size);
  int start = 2 * n + 3;
  int id = 1;
  int cnt = 0;
  for (int i = start; i < size; i += 2) {
    id++;
    if (next[i] == n) {
      pos[++cnt] = id;
    }
  }
  return cnt;
}
int getDistance(int l, int r, int n) {
  if (r >= l)
    return r - l;
  else {
    r = r + n;
    return r - l;
  }
}
Segment toStd(Segment u, int n) {
  int l = u.l, r = u.r;
  int dis = getDistance(l, r, n);
  if (dis * 2 > n) {
    int t = u.l;
    u.l = u.r;
    u.r = t;
  }
  return u;
}
void extraJudge(int n) {
  int size = 0;
  int len = (n / 2);
  for (int i = 1; i <= len; i++) s[++size] = vis[i];
  s[++size] = -1;
  for (int i = 1; i <= n; i++) s[++size] = vis[i];
  for (int i = 1; i <= n; i++) s[++size] = vis[i];
  kmp(size);
  for (int i = len + 2; i <= size; i++) {
    if (next[i] == len) {
      int orgP = i - (len + 1);
      orgP = orgP - len + 1;
      if (orgP > n) orgP -= n;
      good[orgP] = 1;
    }
  }
}
int main() {
  int n, k;
  scanf("%d%d", &n, &k);
  for (int i = 1; i <= n; i++) good[i] = 0, vis[i] = 0;
  int m = 0;
  for (int i = 1; i <= k; i++) {
    int l, r;
    scanf("%d%d", &l, &r);
    if (getDistance(l, r, n) * 2 == n) {
      vis[l] = vis[r] = 1;
    } else {
      m++;
      a[m].l = l, a[m].r = r;
      a[m] = toStd(a[m], n);
    }
  }
  extraJudge(n);
  std::sort(a + 1, a + 1 + m, [&](Segment& u, Segment& v) {
    if (u.l != v.l)
      return u.l < v.l;
    else
      return getDistance(u.l, u.r, n) < getDistance(v.l, v.r, n);
  });
  int size = 0;
  for (int i = 1; i <= m; i++) {
    int u = getDistance(a[i].l, a[i].r, n);
    seq[++size] = u;
    int next = -1;
    if (i != m)
      next = a[i + 1].l;
    else
      next = a[1].l;
    seq[++size] = getDistance(a[i].r, next, n);
  }
  int find = 0;
  if (size == 0)
    for (int i = 2; i <= n; i++) find |= good[i];
  else {
    int offset = a[1].l - 1;
    int all = isSelfMatch(size);
    for (int i = 1; i <= all; i++) {
      int p = a[pos[i]].l - offset;
      if (good[p]) find = 1;
    }
  }
  if (find)
    printf("Yes\n");
  else
    printf("No\n");
  return 0;
}

### Prompt

Create a solution in Cpp for 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>
struct Segment {
  int l, r;
};
Segment a[200005];
int seq[400005];
int s[1200005];
int next[1200005];
int vis[100005];
int good[100005];
int pos[100005];
void kmp(int n) {
  next[1] = 0;
  for (int i = 2; i <= n; i++) {
    int j = next[i - 1];
    while (j != 0 && s[j + 1] != s[i]) j = next[j];
    if (s[j + 1] == s[i]) j++;
    next[i] = j;
  }
}
int isSelfMatch(int n) {
  int size = 0;
  for (int i = 1; i <= n; i++) s[++size] = seq[i];
  s[++size] = 1e9 + 7;
  for (int i = 1; i <= n; i++) s[++size] = seq[i];
  for (int i = 1; i <= n; i++) s[++size] = seq[i];
  kmp(size);
  int start = 2 * n + 3;
  int id = 1;
  int cnt = 0;
  for (int i = start; i < size; i += 2) {
    id++;
    if (next[i] == n) {
      pos[++cnt] = id;
    }
  }
  return cnt;
}
int getDistance(int l, int r, int n) {
  if (r >= l)
    return r - l;
  else {
    r = r + n;
    return r - l;
  }
}
Segment toStd(Segment u, int n) {
  int l = u.l, r = u.r;
  int dis = getDistance(l, r, n);
  if (dis * 2 > n) {
    int t = u.l;
    u.l = u.r;
    u.r = t;
  }
  return u;
}
void extraJudge(int n) {
  int size = 0;
  int len = (n / 2);
  for (int i = 1; i <= len; i++) s[++size] = vis[i];
  s[++size] = -1;
  for (int i = 1; i <= n; i++) s[++size] = vis[i];
  for (int i = 1; i <= n; i++) s[++size] = vis[i];
  kmp(size);
  for (int i = len + 2; i <= size; i++) {
    if (next[i] == len) {
      int orgP = i - (len + 1);
      orgP = orgP - len + 1;
      if (orgP > n) orgP -= n;
      good[orgP] = 1;
    }
  }
}
int main() {
  int n, k;
  scanf("%d%d", &n, &k);
  for (int i = 1; i <= n; i++) good[i] = 0, vis[i] = 0;
  int m = 0;
  for (int i = 1; i <= k; i++) {
    int l, r;
    scanf("%d%d", &l, &r);
    if (getDistance(l, r, n) * 2 == n) {
      vis[l] = vis[r] = 1;
    } else {
      m++;
      a[m].l = l, a[m].r = r;
      a[m] = toStd(a[m], n);
    }
  }
  extraJudge(n);
  std::sort(a + 1, a + 1 + m, [&](Segment& u, Segment& v) {
    if (u.l != v.l)
      return u.l < v.l;
    else
      return getDistance(u.l, u.r, n) < getDistance(v.l, v.r, n);
  });
  int size = 0;
  for (int i = 1; i <= m; i++) {
    int u = getDistance(a[i].l, a[i].r, n);
    seq[++size] = u;
    int next = -1;
    if (i != m)
      next = a[i + 1].l;
    else
      next = a[1].l;
    seq[++size] = getDistance(a[i].r, next, n);
  }
  int find = 0;
  if (size == 0)
    for (int i = 2; i <= n; i++) find |= good[i];
  else {
    int offset = a[1].l - 1;
    int all = isSelfMatch(size);
    for (int i = 1; i <= all; i++) {
      int p = a[pos[i]].l - offset;
      if (good[p]) find = 1;
    }
  }
  if (find)
    printf("Yes\n");
  else
    printf("No\n");
  return 0;
}

```