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.Iterator;
import java.util.Set;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.TreeMap;
import java.util.StringTokenizer;
import java.util.Map;
import java.util.Map.Entry;
import java.io.BufferedReader;
import java.io.InputStream;

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

    static class TaskD {
        TreeMap<Integer, Integer>[] all;
        int N;

        void add(int size, int from) {
            if (all[from] == null)
                all[from] = new TreeMap<>();
            all[from].put(size, all[from].getOrDefault(size, 0) + 1);
        }

        boolean check(int div) {
            for (int i = 0; i < div; i++) {
                for (int num = i + div; num < N; num += div) {
                    if (all[num] == null && all[num - div] == null)
                        continue;
                    if (all[num] == null || all[num - div] == null)
                        return false;
                    if (all[num].entrySet().size() != all[num - div].entrySet().size())
                        return false;
                    Iterator<Map.Entry<Integer, Integer>> it1 = all[num].entrySet().iterator();
                    Iterator<Map.Entry<Integer, Integer>> it2 = all[num - div].entrySet().iterator();
                    while (it1.hasNext()) {
                        Map.Entry<Integer, Integer> e1 = it1.next();
                        Map.Entry<Integer, Integer> e2 = it2.next();
                        if (!e1.getKey().equals(e2.getKey()) || !e1.getValue().equals(e2.getValue())) {
                            return false;
                        }
                    }

                }
            }
            return true;

        }

        public void solve(int testNumber, FastScanner in, PrintWriter out) {

            N = in.ni();
            int M = in.ni();
            all = new TreeMap[N];
            for (int i = 0; i < M; i++) {
                int a = in.ni() - 1, b = in.ni() - 1;
                int left = Math.max(a, b) - Math.min(a, b);
                int right = Math.min(a, b) + N - Math.max(a, b);
                int size = Math.min(left, right);
                if (left < right) {
                    add(size, Math.min(a, b));
                } else if (right < left) {
                    add(size, Math.max(a, b));
                } else {
                    add(size, a);
                    add(size, b);
                }
            }
            for (int div = 1; div * div <= N; div++) {
                if (N % div == 0) {
                    if (check(div)) {
//                    System.out.println("div = " + div);
                        out.println("Yes");
                        return;
                    }
                    if (div * div < N && div != 1) {
                        if (check(N / div)) {
//                        System.out.println("div = " + (N/div));
                            out.println("Yes");
                            return;
                        }
                    }
                }
            }
            out.println("No");
        }

    }

    static class FastScanner {
        private BufferedReader in;
        private StringTokenizer st;

        public FastScanner(InputStream stream) {
            in = new BufferedReader(new InputStreamReader(stream));
        }

        public String ns() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    String rl = in.readLine();
                    if (rl == null) {
                        return null;
                    }
                    st = new StringTokenizer(rl);
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }

        public int ni() {
            return Integer.parseInt(ns());
        }

    }
}

