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 java.util.Scanner;
import java.util.TreeSet;
 
public class fD {
 
	public static void main(String[] args) {
		Scanner stdin = new Scanner(System.in);
		int n = stdin.nextInt();
		int m = stdin.nextInt();
		TreeSet<Integer>[] list = new TreeSet[n];
		for(int i = 0; i < n; i++)
		{
			list[i] = new TreeSet<>(); 
		}
		for(int i = 0; i < m; i++)
		{
			int a = stdin.nextInt();
			int b = stdin.nextInt();
			int temp = Math.max(a, b) - Math.min(a, b);
			int min = Math.min(temp, n-temp);
			list[a-1].add(min);
			list[b-1].add(min);
		}
		int[] hashes = new int[n];
		for(int i = 0; i < n; i++)
		{
			hashes[i] = list[i].hashCode();
		}
		for(int i = 1; i < n; i++)
		{
			boolean rotatable = true;
			for(int u = 0; u < n; u++)
			{
				if(hashes[u] != hashes[(u+i)%n])
				{
					rotatable = false;
					break;
				}
			}
			if(rotatable)
			{
				System.out.println("Yes");
				return;
			}
		}
		System.out.println("No");
		stdin.close();
	}
}