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.BufferedReader;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.LinkedList;
import java.util.List;
import java.util.StringTokenizer;


public class Main {

	static class Task {
		
		int NN = 200005;
		int MOD = 1000000007;
		int INF = 2000000000;
		long INFINITY = 2000000000000000000L;
		
		List<Integer> [] g;
		List<Integer> [] L;
		int tot = 0;
		
		public void solve(InputReader in, PrintWriter out) {
			int n= in.nextInt();
			int m = in.nextInt();
			g = new ArrayList[n + 1];
			for(int i=1;i<=n;++i)
				g[i] = new ArrayList<>();
			for(int i=1;i<=m;++i) {
				int u = in.nextInt();
				int v = in.nextInt();
				g[u].add(v);
				g[v].add(u);
			}
			for(int i=1;i<=n;++i) {
				if(g[i].isEmpty())
					continue;
				++tot;
			}
			L = new ArrayList[tot];
			int idx = -1;
			for(int i=1;i<=n;++i) {
				if(g[i].isEmpty())
					continue;
				L[++idx] = new ArrayList<>();
				for(int e: g[i]) {
					int val= e-i;
					if(val < 0)
						val += n;
					L[idx].add(val);
				}
				L[idx].sort((e1, e2)->e1.compareTo(e2));
			}
			for(int i=1;i*i<=tot;++i) {
				if(tot%i != 0)
					continue;
				int k1 = i;
				int k2 = tot / i;
				if(f(k1)) {
					out.println("Yes");return;
				}
				if(k2 != k1 && k2 != tot && f(k2)) {
					out.println("Yes");return;
				}
			}
			out.println("No");
		}
		
		boolean f(int k) {
			for(int i=k;i<tot;i+=k) {
				for(int j=i;j<i+k;++j) {
					if(!identical(j, j-i))
						return false;					
				}
			}
			return true;
		}
		
		boolean identical(int i, int j) {
			if(L[i].size() != L[j].size())
				return false;
			for(int ii=0;ii<L[i].size();++ii) {
				if(!L[i].get(ii).equals(L[j].get(ii)))
					return false;
			}
			return true;
		}
		
	}
	
	static void prepareIO(boolean isFileIO) {
		//long t1 = System.currentTimeMillis();
		Task solver = new Task();
		// Standard IO
		if(!isFileIO) { 
			InputStream inputStream = System.in;
	        OutputStream outputStream = System.out;
	        InputReader in = new InputReader(inputStream);
	        PrintWriter out = new PrintWriter(outputStream);
	        solver.solve(in, out);
	        //out.println("time(s): " + (1.0*(System.currentTimeMillis()-t1))/1000.0);
	        out.close();
		}
        // File IO
		else {
			String IPfilePath = System.getProperty("user.home") + "/Downloads/ip.in";
	        String OPfilePath = System.getProperty("user.home") + "/Downloads/op.out";
	        InputReader fin = new InputReader(IPfilePath);
	        PrintWriter fout = null;
	        try {
				fout = new PrintWriter(new File(OPfilePath));
			} catch (FileNotFoundException e) {
				e.printStackTrace();
			}
	        solver.solve(fin, fout);
	        //fout.println("time(s): " + (1.0*(System.currentTimeMillis()-t1))/1000.0);
	        fout.close();
		}
	}
	
	public static void main(String[] args) {
        prepareIO(false);
	}
	
	static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
        
        public InputReader(String filePath) {
        	File file = new File(filePath);
            try {
				reader = new BufferedReader(new FileReader(file));
			} catch (FileNotFoundException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
            tokenizer = null;
        }
        
        public String nextLine() {
        	String str = "";
        	try {
				str = reader.readLine();
			} catch (IOException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
        	return str;
        }
        
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
        	return Double.parseDouble(next());
        }
        
    }

}