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.nio.CharBuffer;
import java.util.HashMap;
import java.util.NoSuchElementException;

public class P1162D {

    public static void main(String[] args) {
        SimpleScanner scanner = new SimpleScanner(System.in);
        PrintWriter writer = new PrintWriter(System.out);

        int n = scanner.nextInt();
        int m = scanner.nextInt();
        int[][] segments = new int[m][2];
        HashMap<Integer, Integer>[] segSets = new HashMap[n];
        for (int i = 0; i < m; ++i) {
            segments[i][0] = scanner.nextInt() - 1;
            segments[i][1] = scanner.nextInt() - 1;
            if (segSets[segments[i][0]] == null)
                segSets[segments[i][0]] = new HashMap<>();
            segSets[segments[i][0]].put(segments[i][1], i);
            if (segSets[segments[i][1]] == null)
                segSets[segments[i][1]] = new HashMap<>();
            segSets[segments[i][1]].put(segments[i][0], i);
        }
        boolean valid = testSeg(segments, segSets, 1, n, m);
        int k;
        for (k = 2; !valid && k * k < n; ++k)
            valid = n % k == 0 && (testSeg(segments, segSets, k, n, m) || testSeg(segments, segSets, n / k, n, m));
        valid = valid || (k * k == n && testSeg(segments, segSets, k, n, m));
        writer.println(valid ? "Yes" : "No");
        writer.close();
    }

    private static boolean testSeg(int[][] segments, HashMap<Integer, Integer>[] segSets, int k, int n, int m) {
        boolean[] visited = new boolean[m];
        for (int i = 0; i < m; ++i) {
            if (visited[i])
                continue;
            int x = (segments[i][0] + k) % n;
            int y = (segments[i][1] + k) % n;
            while (x != segments[i][0]) {
                Integer idx = segSets[x] == null ? null : segSets[x].get(y);
                if (idx == null)
                    idx = segSets[y] == null ? null : segSets[y].get(x);
                if (idx == null)
                    return false;
                visited[idx] = true;
                x = (x + k) % n;
                y = (y + k) % n;
            }
            visited[i] = true;
        }
        return true;
    }

    private static class SimpleScanner {

        private static final int BUFFER_SIZE = 10240;

        private Readable in;
        private CharBuffer buffer;
        private boolean eof;

        SimpleScanner(InputStream in) {
            this.in = new BufferedReader(new InputStreamReader(in));
            buffer = CharBuffer.allocate(BUFFER_SIZE);
            buffer.limit(0);
            eof = false;
        }


        private char read() {
            if (!buffer.hasRemaining()) {
                buffer.clear();
                int n;
                try {
                    n = in.read(buffer);
                } catch (IOException e) {
                    n = -1;
                }
                if (n <= 0) {
                    eof = true;
                    return '\0';
                }
                buffer.flip();
            }
            return buffer.get();
        }

        void checkEof() {
            if (eof)
                throw new NoSuchElementException();
        }

        char nextChar() {
            checkEof();
            char b = read();
            checkEof();
            return b;
        }

        String next() {
            char b;
            do {
                b = read();
                checkEof();
            } while (Character.isWhitespace(b));
            StringBuilder sb = new StringBuilder();
            do {
                sb.append(b);
                b = read();
            } while (!eof && !Character.isWhitespace(b));
            return sb.toString();
        }

        int nextInt() {
            return Integer.valueOf(next());
        }

        long nextLong() {
            return Long.valueOf(next());
        }

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