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 void solve() throws IOException {
        int n = nextInt();
        int m = nextInt();
        TreeSet<Integer>[] ch = new TreeSet[n];
        for (int i = 0; i < n; i++) {
            ch[i] = new TreeSet<>();
        }
        for (int i = 0; i < m; i++) {
            int a = nextInt() - 1;
            int b = nextInt() - 1;
            if (a > b) {
                int t = a;
                a = b;
                b = t;
            }
            if (b - a == n + a - b) {
                ch[b - a].add(a);
                ch[b - a].add(b);
            } else if (b - a < n + a - b)
                ch[b - a].add(a);
            else ch[n + a - b].add(b);
        }
        ArrayList<Integer> d = new ArrayList<>();
        d.add(1);
        for (int i = 2; i * i <= n; i++) {
            if (n % i == 0) {
                d.add(i);
                d.add(n / i);
            }
        }
        if (d.isEmpty()) {
            System.out.println("No");
            return;
        }
        for (int i = 0; i < d.size(); i++) {
            int cur = d.get(i);
            boolean good = true;
            for (int j = 0; j < n; j++) {
                for (int v : ch[j]) {
                    if (!ch[j].contains((v + cur) % n)) {
                        good = false;
                    }
                }
            }
            if (good) {
                System.out.println("Yes");
                return;
            }
        }
        System.out.println("No");
    }

    public void run() {
        try {
            br = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);

            solve();

            out.close();
        } catch (IOException e) {
            e.printStackTrace();
            System.exit(1);
        }
    }

    BufferedReader br;
    StringTokenizer in;
    PrintWriter out;

    public String nextToken() throws IOException {
        while (in == null || !in.hasMoreTokens()) {
            in = new StringTokenizer(br.readLine());
        }
        return in.nextToken();
    }

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

    public double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    public long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    public int[] nextArr(int n) throws IOException {
        int[] res = new int[n];
        for (int i = 0; i < n; i++) {
            res[i] = nextInt();
        }
        return res;
    }

    public static void main(String[] args) throws IOException {
        Locale.setDefault(Locale.US);
        new D().run();
    }
}