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.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.StringTokenizer;

public class Solution {
    private FastScanner in;
    private PrintWriter out;

    public static void main(String[] args) {
        (new Solution()).run();
    }

    private void run() {
        try {
            in = new FastScanner(System.in);
            out = new PrintWriter(System.out);
            solution();
            out.close();
            in.close();
        } catch (Exception e) {
            e.printStackTrace();
        }
    }

    private void solution() throws IOException {
        int n = in.nextInt();
        int m = in.nextInt();
        List<List<Integer>> data = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            data.add(new ArrayList<>());
        }
        while (m-- > 0) {
            int a = in.nextInt() - 1;
            int b = in.nextInt() - 1;
            data.get(a).add((b - a + n) % n);
            data.get(b).add((a - b + n) % n);
        }
        for (int i = 0; i < n; i++) {
            Collections.sort(data.get(i));
        }
        //out.println(data);
        for (int t = 2; t * t <= n; t++) {
            if (n % t == 0) {
                int t1 = n / t;
                boolean res = true;
                boolean res1 = true;
                for (int i = 0; i < n - t; i++) {
                    res &= equal(data.get(i), data.get(i + t));
                }
                for (int i = 0; i < n - t1; i++) {
                    res1 &= equal(data.get(i), data.get(i + t1));
                }
                if(res||res1){
                    out.println("Yes");
                    return;
                }
            }
        }
        boolean res = true;
        for (int i = 0; i < n - 1; i++) {
            res &= equal(data.get(i), data.get(i + 1));
        }
        out.println(res?"Yes":"No");
    }

    private boolean equal(List<Integer> a, List<Integer> b) {
        if (a.size() != b.size()) return false;
        for (int i = 0; i < a.size(); i++) {
            if (!a.get(i).equals(b.get(i))) return false;
        }
        return true;
    }

    private class FastScanner {
        BufferedReader bufferedReader;
        StringTokenizer stringTokenizer;

        FastScanner(InputStream inputStream) {
            bufferedReader = new BufferedReader(new InputStreamReader(inputStream));
        }

        public String next() throws IOException {
            while (stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
                String temp = bufferedReader.readLine();
                if (temp == null) {
                    return null;
                }
                stringTokenizer = new StringTokenizer(temp);
            }
            return stringTokenizer.nextToken();
        }

        public String nextLine() throws IOException {
            return bufferedReader.readLine();
        }

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

        public void close() throws IOException {
            bufferedReader.close();
        }
    }
}

