CF1147B.Chladni Figure

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 $i + 1$ ($1 \leq i \lt n$) 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 $k$ ($1 \leq k \lt n$), 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.

伊纳卡有一个圆盘，其周长为 $n$ 个单位。该圆周被 $n$ 个点等距划分，这些点按顺时针方向编号为 $1$ 至 $n$，使得点 $i$ 与点 $i + 1$（其中 $1 \leq i < n$）相邻，且点 $n$ 与点 $1$ 也相邻。

圆盘上有 $m$ 条直线段，每条线段的两个端点均来自上述 $n$ 个点。

伊纳卡想知道她的图像是否具有旋转对称性，即：是否存在一个整数 $k$（满足 $1 \leq k < n$），使得将所有线段绕圆心顺时针旋转 $k$ 个单位后，所得新图像与原图像完全相同。

The first line contains two space-separated integers $n$ and $m$ ($2 \leq n \leq 100\,000$, $1 \leq m \leq 200\,000$) — 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 $b_i$ ($1 \leq a_i, b_i \leq n$, $a_i \neq b_i$) that describe a segment connecting points $a_i$ and $b_i$.

It is guaranteed that no segments coincide.

第一行包含两个用空格分隔的整数 $n$ 和 $m$（$2 \leq n \leq 100\,000$，$1 \leq m \leq 200\,000$），分别表示点的数量和线段的数量。

接下来的 $m$ 行中，第 $i$ 行包含两个用空格分隔的整数 $a_i$ 和 $b_i$（$1 \leq a_i, b_i \leq n$，$a_i \neq b_i$），描述一条连接点 $a_i$ 和 $b_i$ 的线段。

保证不存在重合的线段。

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).

输出一行——如果该图像具有旋转对称性，则输出“Yes”，否则输出“No”（均不包含引号）。

每个字母可以以任意大小写形式输出（大写或小写）。

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.

前两个示例在下方图示中给出。两张图片分别绕中心顺时针旋转 $120$ 度后，均与各自的原始图像完全相同。