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>
import sys
def No():
    print('No')
    sys.exit()
def divi(n):
    res = [1]
    for i in range(2, int(n**0.5)+1):
        if n % i == 0:
            res.append(i)
            if i != n // i:
                res.append(n//i)
    return res
N, M = map(int, input().split())
DN = divi(N)
dis = [set() for _ in range(N//2 + 1)]
for i in range(M):
    a, b = map(lambda x:int(x) - 1, sys.stdin.readline().split())
    fn, ln = (a - b)%N, (b - a)%N
    if fn < ln:
        dis[fn].add(b)
    elif ln < fn:
        dis[ln].add(a)
    else:
        dis[fn].add(a)
        dis[fn].add(b)
for dn in DN:
    for D in dis:
        if not D:
            continue
        for d in D:
            if (d+dn)%N not in D:
                break
        else:
            continue
        break
    else:
        print('Yes')
        sys.exit()
No()