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.*;

import static java.lang.Integer.parseInt;
import static java.nio.charset.StandardCharsets.UTF_8;

public class Main {

    public static void main(String[] args) throws IOException {
        try (BufferedReader in = new BufferedReader(new InputStreamReader(System.in, UTF_8));
             BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out, UTF_8))) {
            StringTokenizer tokens = new StringTokenizer(in.readLine());
            int n = parseInt(tokens.nextToken());
            int m = parseInt(tokens.nextToken());
            Set<Pair> chords = new HashSet<>();
            for (int i = 0; i < m; i++) {
                tokens = new StringTokenizer(in.readLine());
                int x = parseInt(tokens.nextToken()) - 1;
                int y = parseInt(tokens.nextToken()) - 1;
                chords.add(new Pair(x, y));
            }
            List<Integer> divs = findDivs(n);
            boolean success = false;
            for (int div : divs) {
                boolean ok = true;
                for (Pair chord : chords) {
                    int x = (chord.x + div) % n;
                    int y = (chord.y + div) % n;
                    Pair pair = new Pair(x, y);
                    if (!chords.contains(pair)) {
                        ok = false;
                        break;
                    }
                }
                if (ok) {
                    success = true;
                    break;
                }
            }
            out.write(success ? "Yes" : "No");
        }
    }

    private static List<Integer> findDivs(int n) {
        List<Integer> divs = new ArrayList<>();
        for (int i = 1; i < n; i++) {
            if (n % i == 0) {
                divs.add(i);
            }
        }
        return divs;
    }

    private static class Pair {

        final int x;
        final int y;

        public Pair(int x, int y) {
            this.x = x < y ? x : y;
            this.y = x < y ? y : x;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Pair pair = (Pair) o;
            return x == pair.x &&
                    y == pair.y;
        }

        @Override
        public int hashCode() {
            return Objects.hash(x, y);
        }
    }
}
