B. Chladni Figuretime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputInaka 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.InputThe 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.OutputOutput 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).ExamplesInput
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
NoteThe 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.  
12 6
1 3
3 7
5 7
7 11
9 11
11 3

Yes 
['brute force', 'strings', '*1900']