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>
n, m = map(int, input().split())
a = []
for i in range(m):
    a.append(list(map(int, input().split())))
    if (a[i][0] > a[i][1]):
        a[i][0], a[i][1] = a[i][1], a[i][0]
    if (a[i][1] - a[i][0] > n / 2):
        a[i][0] += n
        a[i][0], a[i][1] = a[i][1], a[i][0]

if (m == 1):
    if (a[0][1] - a[0][i] == n / 2):
        print("Yes")
    else:
        print("No")
    exit(0)
    
a.sort()
for i in range(m):
    a.append([a[i][0] + n, a[i][1] + n])
b = []
for i in range(2 * m - 1):
    if (a[i][1] - a[i][0] == n / 2):
        b.append((a[i][1] - a[i][0], min(a[i + 1][0] - a[i][0], n - a[i + 1][0] + a[i][0])))
    else:
        b.append((a[i][1] - a[i][0], a[i + 1][0] - a[i][0]))

# Z function
z = [0] * 2 * m
l = r = 0

for i in range(1, m):
    if (i <= r):
        z[i] = min(z[i - l], r - i + 1)
    while (i + z[i] < len(b) and b[i + z[i]] == b[z[i]]):
        z[i] += 1
    if (i + z[i] - 1 > r):
        l = i
        r = i + z[i] - 1
    if (z[i] >= m):
        print("Yes")
        exit(0)

print("No")
