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>
//Created by Aminul on 5/5/2019.

import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Comparator;
import java.util.Scanner;

import static java.lang.Math.max;
import static java.lang.Math.min;

public class D_3 {
    public static void main(String[] args) throws Exception {
        Scanner in = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int n = in.nextInt(), m = in.nextInt();
        int pairs[][] = new int[m][2];
        for (int i = 0; i < m; i++) {
            int u = in.nextInt() - 1, v = in.nextInt() - 1;
            pairs[i][0] = min(u, v);
            pairs[i][1] = max(u, v);
        }

        final Comparator cmp = new Comparator<int[]>() {
            public int compare(int[] a, int[] b) {
                if (a[0] == b[0]) return a[1] - b[1];
                return a[0] - b[0];
            }
        };
        Arrays.sort(pairs, cmp);

        boolean ok = false;
        int tmp[][] = new int[m][2];
        for (int i = 1; i < n; i++) {
            if (n % i != 0) continue;
            int k = 0;
            for (int a[] : pairs) {
                int x = (a[0] + i), y = (a[1] + i);
                if (x >= n) x -= n;
                if (y >= n) y -= n;
                tmp[k][0] = min(x, y);
                tmp[k][1] = max(x, y);
                k++;
            }
            Arrays.sort(tmp, cmp);
            boolean equal = true;
            for (k = 0; k < m && equal; k++) {
                equal &= (tmp[k][0] == pairs[k][0] && tmp[k][1] == pairs[k][1]);
            }
            ok |= equal;
        }

        if (ok) pw.println("Yes");
        else pw.println("No");

        pw.close();
    }

    static void debug(Object... obj) {
        System.err.println(Arrays.deepToString(obj));
    }
}