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>
def gcd(x,y):
	while y:
		x,y = y,x%y
	return x
def lcm(a,b): return (a*b)//gcd(a,b)

import io,os
input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline
kk=lambda:map(int,input().split())
k2=lambda:map(lambda x:int(x)-1, input().split())
ll=lambda:list(kk())
n,m=kk()
nodes = [[] for _ in range(n)]
for _ in range(m):
	n1,n2=k2()
	nodes[n1].append((n2-n1)%n)
	nodes[n2].append((n1-n2)%n)
seen = {}
nextv=0
lists = []
node2,used = [0]*n, [False]*n
for i,no in enumerate(nodes):
	t = tuple(sorted(no))
	if not t in seen: 
		seen[t],nextv = nextv,nextv+1
		lists.append([])
	lists[seen[t]].append(i)
	node2[i] = seen[t]
lists.sort(key=len)
valids = set()
for i in range(nextv-1):
	cl = lists[i]
	n0 = cl[0]
	continueing = True
	while continueing:
		continueing = False
		for j in range(1,len(cl)):
			if used[cl[j]]: continue
			dist = cl[j]-n0
			if n%dist != 0: continue
			for k in range(n0, n+n0, dist):
				k = k%n
				if used[k] or node2[k] != node2[n0]:
					break
			else:
				# we found a working one.
				valids.add(dist)
				for k in range(n0, n+n0, dist):
					k = k%n
					used[k]=True
				cl = [x for x in cl if (x-n0)%dist != 0]
				n0 = cl[0] if cl else 0
				continueing= True
				break
	if len(cl) > 0:
		print("NO")
		exit()
lc =1
for value in valids:
	lc = lcm(lc, value)
print("YES" if lc< n else "NO")