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.io.*;
import java.util.*;

public class D2 {
	
	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(br.readLine());
//		Scanner seer = new Scanner(System.in);
		int n = Integer.parseInt(st.nextToken());
		int m = Integer.parseInt(st.nextToken());
		
		int[] sieve = new int[n+1];
		for(int i = 2; i <= n; i++){
			if(sieve[i] == 0){
				sieve[i] = i;
				if((long)i*(long)i > (long)n) continue;
				for(int j = i*i; j <= n; j+=i){
					sieve[j] = i;
				}
			}
		}
		HashSet<Pair> ps = new HashSet<Pair>();
		for(int i = 0; i < m; i++){
			st = new StringTokenizer(br.readLine());
			int a = Integer.parseInt(st.nextToken())-1;
			int b = Integer.parseInt(st.nextToken())-1;
			ps.add(new Pair(Integer.min(a, b), Integer.max(a, b)));
		}
		HashSet<Integer> divs = new HashSet<>();
		int aux = n;
		while(aux > 1){
			divs.add(sieve[aux]);
			aux /= sieve[aux];
		}
		boolean fits = false;
		for(int div: divs){
			int k = n/div;
			fits = true;
			for(Pair p: ps){
				int a = (p.a+k)%n;
				int b = (p.b+k)%n;
				Pair look = new Pair(Integer.min(a, b), Integer.max(a, b));
				if(!ps.contains(look)){
					fits = false; break;
				}
			}
			if(fits) break;
		}
		if(fits) System.out.println("Yes");
		else System.out.println("No");
	}
	static class Pair{
		int a, b;
		public Pair(int a, int b){
			this.a = a; this.b = b;
		}
		public String toString(){
			return a+","+b;
		}
		@Override
		public boolean equals(Object o){
			Pair p = (Pair)o;
			return p.a == a && p.b == b;
		}
		@Override
		public int hashCode(){
			return a+b;
		}
	}

}
