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.Arrays;
import java.util.NoSuchElementException;
import java.util.TreeSet;

public class P1162D_2 {

    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();
        @SuppressWarnings("unchecked")
        TreeSet<Integer>[] segments = new TreeSet[n];
        int size = n + m * 2;
        for (int i = 0; i < m; ++i) {
            int x = scanner.nextInt() - 1;
            int y = scanner.nextInt() - 1;
            int min = Math.min(x, y);
            int max = Math.max(x, y);
            if (segments[min] == null) {
                segments[min] = new TreeSet<>();
                --size;
            }
            if (segments[max] == null) {
                segments[max] = new TreeSet<>();
                --size;
            }
            segments[min].add(max - min);
            segments[max].add(min - max + n);
        }
        int[] s = new int[size];
        for (int i = 0, k = 0; i < n; ++i) {
            if (segments[i] == null) {
                s[k++] = 0;
            } else {
                for (int j : segments[i]) {
                    s[k++] = j;
                }
            }
        }
//        System.out.println(Arrays.toString(s));
        int[] z = new int[size];
        for (int i = 1, l = 0, r = 0; i < size; ++i) {
            if (i <= r)
                z[i] = Math.min(z[i - l], r - i + 1);
            while (z[i] < size && s[z[i]] == s[(i + z[i]) % size])
                ++z[i];
            if (z[i] == size) {
                writer.println("Yes");
                writer.close();
                return;
            }
            if (i + z[i] - 1 > r)
                r = i + z[i] - 1;
        }
        writer.println("No");
        writer.close();
    }

    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());
        }
    }
}
