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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.util.Random;
import java.math.BigInteger;
import java.io.IOException;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author NMouad21
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DChladniFigure solver = new DChladniFigure();
        solver.solve(1, in, out);
        out.close();
    }

    static class DChladniFigure {
        private int n;
        private int m;
        private ArrayList<Integer>[] a;
        private long[] hash;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            n = in.nextInt();
            m = in.nextInt();

            a = new ArrayList[n + 1];
            hash = new long[n + 1];
            for (int i = 0; i <= n; i++) {
                a[i] = new ArrayList<>();
            }

            for (int i = 1; i <= m; i++) {
                int x = in.nextInt();
                int y = in.nextInt();
                a[x].add(dist(x, y));
                a[y].add(dist(y, x));
            }
            hashAll();

            long[] a = new long[(n + 1) * 3];
            for (int i = 1; i <= n; i++) {
                a[i - 1] = a[i + n] = a[i + n * 2] = hash[i];
            }
            a[n] = -1;

            int[] f = new int[a.length];
            for (int i = 1, border = 0; i < a.length; ++i) {
                while (border > 0 && a[border] != a[i])
                    border = f[border - 1];
                if (a[border] == a[i]) {
                    ++border;
                }
                f[i] = border;
            }

            for (int i = n * 2 + 1; i < n * 3; i++) {
                if (f[i] == n) {
                    out.println("Yes");
                    return;
                }
            }
            out.println("No");
        }

        private void hashAll() {
            final Random r = new Random();
            final int b1 = n + r.nextInt(5);
            final int b2 = (b1 + 1) + r.nextInt(4);
            final int m1 = new BigInteger(((int) 1e9 + 9) + "").nextProbablePrime().intValue();
            final int m2 = new BigInteger((m1 + 1) + "").nextProbablePrime().intValue();

            for (int i = 1; i <= n; i++) {
                if (!a[i].isEmpty()) {
                    long h1 = 0, h2 = 0;
                    a[i].sort(null);
                    for (int x : a[i]) {
                        h1 = (h1 * b1 + x) % m1;
                        h2 = (h2 * b2 + x) % m2;
                    }
                    hash[i] = (h1 << 32) | h2;
                }
            }
        }

        private int dist(int o, int x) {
            if (x > o) {
                return x - o;
            }
            return (n + x) - o;
        }

    }

    static class InputReader {
        private InputStream stream;
        private static final int DEFAULT_BUFFER_SIZE = 1 << 16;
        private static final int EOF = -1;
        private byte[] buf = new byte[DEFAULT_BUFFER_SIZE];
        private int curChar;
        private int numChars;

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

        public int read() {
            if (this.numChars == EOF) {
                throw new UnknownError();
            } else {
                if (this.curChar >= this.numChars) {
                    this.curChar = 0;

                    try {
                        this.numChars = this.stream.read(this.buf);
                    } catch (IOException ex) {
                        throw new InputMismatchException();
                    }

                    if (this.numChars <= 0) {
                        return EOF;
                    }
                }

                return this.buf[this.curChar++];
            }
        }

        public int nextInt() {
            int c;
            for (c = this.read(); isSpaceChar(c); c = this.read()) {
            }

            byte sgn = 1;
            if (c == 45) {
                sgn = -1;
                c = this.read();
            }

            int res = 0;

            while (c >= 48 && c <= 57) {
                res *= 10;
                res += c - 48;
                c = this.read();
                if (isSpaceChar(c)) {
                    return res * sgn;
                }
            }

            throw new InputMismatchException();
        }

        public static boolean isSpaceChar(int c) {
            return c == 32 || c == 10 || c == 13 || c == 9 || c == EOF;
        }

    }
}

