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 D {

    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);
        Solver solver = new Solver();
        solver.solve(in, out);
        out.close();
    }

    private static class Solver {

        private class Pair {
            int a, b;

            public Pair(int a, int b) {
                this.a = a;
                this.b = b;
            }

            @Override
            public boolean equals(Object o) {
                if (this == o) return true;
                if (!(o instanceof Pair)) return false;
                Pair p = (Pair) o;
                return (a == p.a) && (b == p.b);
            }

            @Override
            public int hashCode() {
                return 31 * Integer.valueOf(a).hashCode() + Integer.valueOf(b).hashCode();
            }
        }

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

            Set<Integer> divs = new TreeSet<>();
            Set<Pair> segs = new HashSet<>();

            for (int i = 1; i < n; i++) {
                if (n % i == 0)
                    divs.add(i);
            }

            for (int i = 0; i < m; i++) {
                int a = in.nextInt() - 1;
                int b = in.nextInt() - 1;
                if (a < b)
                    segs.add(new Pair(a, b));
                else
                    segs.add(new Pair(b, a));
            }

            for (int d : divs) {
                boolean lev = true;
                for (Pair p : segs) {
                    int a = (p.a + d) % n;
                    int b = (p.b + d) % n;
                    if (!segs.contains(new Pair(a, b)) && !segs.contains(new Pair(b, a))) {
                        lev = false;
                        break;
                    }
                }
                if (lev) {
                    out.println("Yes");
                    return;
                }
            }
            out.println("No");
        }
    }

    private static class InputReader {
        private BufferedReader br;
        private StringTokenizer st;

        public InputReader(InputStream stream) {
            br = new BufferedReader(new InputStreamReader(stream));
        }

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

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

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

        private String nextLine() {
            String s = "";
            try {
                s = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return s;
        }

        private String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
    }
}