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>
/**
 * @author derrick20
 */
import java.io.*;
import java.util.*;

public class ChladniFigure {
    public static void main(String args[]) throws Exception {
        FastScanner sc = new FastScanner();
        PrintWriter out = new PrintWriter(System.out);

        N = sc.nextInt();
        int M = sc.nextInt();
        Line[] arr = new Line[N];
        HashMap<Integer, TreeSet<Integer>> groups = new HashMap<>();
        for (int i = 0; i < M; i++) {
            int a = sc.nextInt() - 1;
            int b = sc.nextInt() - 1;
            int d1 = (b - a + N) % N;
            int d2 = N - d1;
            int d;
            int start;
            if (d1 < d2) {
                d = d1;
                start = a;
            }
            else {
                d = d2;
                start = b;
            }

            if (groups.containsKey(d)) {
                groups.get(d).add(start);
            }
            else {
                TreeSet<Integer> f = new TreeSet<>();
                f.add(start);
                groups.put(d, f);
            }
        }

        ArrayList<Integer> factors = new ArrayList<>();
        factors.add(1);
        int X = N;
        for (int i = 2; i <= N / 2; i++) {
            if (X % i == 0) {
                factors.add(i);
            }
        }

        boolean poss = false;
        for (int factor : factors) {
            boolean works = true;
            for (int d : groups.keySet()) {
                TreeSet<Integer> l = groups.get(d);
//                System.out.println(factor + " " + l);
                for (int a : l) {
                    if (!l.contains((a + factor) % N) && !(2 * factor == N && 2 * d == N)) {
                        works = false;
                        break;
                    }
                }
            }
            if (works) {
                poss = true;
                break;
            }
        }

        out.println(poss ? "Yes" : "No");
        out.close();
    }

    static int N;

    static class Line implements Comparable<Line> {
        int a, b, d;
        public Line(int start, int end) {
            a = start;
            b = end;
            d = (end - start + N) % N;
        }
        public int compareTo(Line l2) {
            return a - l2.a;
        }
        public String toString() {
            return "(" + a + ", " +  b + ")";
        }
    }

    static class FastScanner {
        public int BS = 1<<16;
        public char NC = (char)0;
        byte[] buf = new byte[BS];
        int bId = 0, size = 0;
        char c = NC;
        double cnt = 1;
        BufferedInputStream in;

        public FastScanner() {
            in = new BufferedInputStream(System.in, BS);
        }

        public FastScanner(String s) {
            try {
                in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
            }
            catch (Exception e) {
                in = new BufferedInputStream(System.in, BS);
            }
        }

        private char getChar(){
            while(bId==size) {
                try {
                    size = in.read(buf);
                }catch(Exception e) {
                    return NC;
                }
                if(size==-1)return NC;
                bId=0;
            }
            return (char)buf[bId++];
        }

        public int nextInt() {
            return (int)nextLong();
        }

        public int[] nextInts(int N) {
            int[] res = new int[N];
            for (int i = 0; i < N; i++) {
                res[i] = (int) nextLong();
            }
            return res;
        }

        public long[] nextLongs(int N) {
            long[] res = new long[N];
            for (int i = 0; i < N; i++) {
                res[i] = nextLong();
            }
            return res;
        }

        public long nextLong() {
            cnt=1;
            boolean neg = false;
            if(c==NC)c=getChar();
            for(;(c<'0' || c>'9'); c = getChar()) {
                if(c=='-')neg=true;
            }
            long res = 0;
            for(; c>='0' && c <='9'; c=getChar()) {
                res = (res<<3)+(res<<1)+c-'0';
                cnt*=10;
            }
            return neg?-res:res;
        }

        public double nextDouble() {
            double cur = nextLong();
            return c!='.' ? cur:cur+nextLong()/cnt;
        }

        public String next() {
            StringBuilder res = new StringBuilder();
            while(c<=32)c=getChar();
            while(c>32) {
                res.append(c);
                c=getChar();
            }
            return res.toString();
        }

        public String nextLine() {
            StringBuilder res = new StringBuilder();
            while(c<=32)c=getChar();
            while(c!='\n') {
                res.append(c);
                c=getChar();
            }
            return res.toString();
        }

        public boolean hasNext() {
            if(c>32)return true;
            while(true) {
                c=getChar();
                if(c==NC)return false;
                else if(c>32)return true;
            }
        }
    }
}