A12517 | 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 $i + 1$ ( $1 \leq i < n$ ) 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 $k$ ( $1 \leq k < n$ ), 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.

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.

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).