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 javafx.scene.layout.Priority;
import java.io.*;
import java.lang.reflect.Array;
import java.net.Inet4Address;
import java.util.*;
import java.lang.*;
import java.util.HashMap;
import java.util.PriorityQueue;
public class templ implements Runnable {
    static class pair implements Comparable
    {
        int f;
        int s;
        pair(int fi,int se)
        {
            f=fi;
            s=se;
        }
        public int compareTo(Object o)
        {
            pair pr=(pair)o;
            if(s>pr.s)
                return 1;
            if(s==pr.s)
            {
                if(f<pr.f)
                    return 1;
                else
                    return -1;
            }
            else
                return -1;
        }
        public boolean equals(Object o)
        {
            pair ob=(pair)o;
            int ff;
            int ss;
            if(o!=null)
            {
                ff=ob.f;
                ss=ob.s;
                if((ff==this.f)&&(ss==this.s))
                    return true;
            }
            return false;
        }
        public int hashCode()
        {
            return (this.f+" "+this.s).hashCode();
        }
    }
    public class triplet implements Comparable
    {
        int f,t;
        int s;
        triplet(int f,int s,int t)
        {
            this.f=f;
            this.s=s;
            this.t=t;
        }
        public boolean equals(Object o)
        {
            triplet ob=(triplet)o;
            int ff;
            int ss;
            int tt;
            if(o!=null)
            {
                ff=ob.f;
                ss=ob.s;
                tt=ob.t;
                if((ff==this.f)&&(ss==this.s)&&(tt==this.t))
                    return true;
            }
            return false;
        }
        public int hashCode()
        {
            return (this.f+" "+this.s+" "+this.t).hashCode();
        }
        public int compareTo(Object o)
        {
            triplet tr=(triplet)o;
            if(t>tr.t)
                return 1;
            else
                return -1;
        }
    }
    ArrayList<Integer>al=new ArrayList<>();
    void KMPSearch(String pat, String txt)
    {
        int M = pat.length();
        int N = txt.length();
        int lps[] = new int[M];
        int j = 0;
        computeLPSArray(pat, M, lps);

        int i = 0;
        while (i < N) {
            if (pat.charAt(j) == txt.charAt(i)) {
                j++;
                i++;
            }
            if (j == M) {
                al.add(i-j);
                j = lps[j - 1];
            }
            else if (i < N && pat.charAt(j) != txt.charAt(i)) {
                if (j != 0)
                    j = lps[j - 1];
                else
                    i = i + 1;
            }
        }
    }
    void computeLPSArray(String pat, int M, int lps[])
    {
        int len = 0;
        int i = 1;
        lps[0] = 0;
        while (i < M) {
            if (pat.charAt(i) == pat.charAt(len)) {
                len++;
                lps[i] = len;
                i++;
            }
            else
            {
                if (len != 0) {
                    len = lps[len - 1];
                }
                else
                {
                    lps[i] = len;
                    i++;
                }
            }
        }
    }
    public static void main(String args[])throws Exception
    {
        new Thread(null,new templ(),"templ",1<<27).start();
    }
    public void run()
    {
        try
        {
            InputReader in = new InputReader(System.in);
            PrintWriter out = new PrintWriter(System.out);
            int n=in.ni();
            int m=in.ni();
            ArrayList<Integer>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.ni();
                int v=in.ni();
                g[u].add((v-u+n)%n);
                g[v].add((u-v+n)%n);
            }
            for(int i=1;i<=n;i++)
                Collections.sort(g[i]);
            StringBuilder sb1=new StringBuilder();
            for(int i=1;i<=n;i++)
            {
                sb1.append("0,");
                for(int j : g[i])
                    sb1.append(j+",");
            }
            StringBuilder sb2=new StringBuilder(sb1);
            sb2.append(sb1);
            String text=sb2.toString();
            String pattern=sb1.toString();
            pattern=","+pattern;
            //out.println(pattern);
            //out.println(text);
            KMPSearch(pattern,text);
            //out.println(al.size());
            if(al.size()>1)
                out.println("YES");
            else
                out.println("NO");
            out.close();
        }
        catch(Exception e){
            return;
        }
    }
    static class InputReader {

        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) {
                curChar = 0;
                try {
                    snumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int ni() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nl() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int[] nextIntArray(int n) {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public String nextLine() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

    }
}