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.util.*;
import java.io.*;

public class d {
    public static void main(String[] args) throws Exception{
        FS sc = new FS(System.in);
        int n = sc.nextInt();
        int lines = sc.nextInt(), i, j;
        ArrayList<Integer>[] adj = new ArrayList[n];
        for (i = 0; i < n; i++)
            adj[i] = new ArrayList<Integer>();
        for (i = 0; i < lines; i++) {
            int a = sc.nextInt() - 1;
            int b = sc.nextInt() - 1;
            adj[a].add(b);
            adj[b].add(a);
        }
        //Random r = new Random(System.currentTimeMillis());
        Random r = new Random(1234);
        int[] mod = new int[2];
        int mf = n + 1;
        mod[0] = r.nextInt(n + 10) + n + 10;
        while (gcd(mf, mod[0]) != 1)
            mod[0] = r.nextInt(n + 10) + n + 10;
        mod[1] = r.nextInt(n + 10) + n + 10;
        while (gcd(mod[0], mod[1]) != 1 || gcd(mf, mod[1]) != 1)
            mod[1] = r.nextInt(n + 10) + n + 10;
        long[][] pows = new long[2][n + 10];
        for (j = 0; j < 2; j++){
            pows[j][0] = 1;
            for (i = 1; i < n + 10; i++) {
                pows[j][i] = pows[j][i - 1] * mf;
                pows[j][i] %= mod[j];
            }
        }
        long[] oldHash = new long[2];
        long[] curHash = new long[2];
        for (i = 0; i < n; i++) {
            for (Integer x : adj[i]) {
                if (x > i) {
                    for (j = 0; j < 2; j++) {
                        oldHash[j] += pows[j][i] * (x - i);
                        oldHash[j] %= mod[j];
                    }
                }
            }
        }
        for (j = 0; j < 2; j++)
            curHash[j] = oldHash[j];
        
        for (i = n - 1; i >= 1; i--) {
            for (j = 0; j < 2; j++) {
                // subtract
                for (Integer x : adj[i]) {
                    int y = x;
                    if (y > i)
                        y -= n;
                    curHash[j] -= (pows[j][n-1 - (i - y)] * (i - y)) % mod[j];
                }
                curHash[j] %= mod[j];
                if (curHash[j] < 0)
                    curHash[j] += mod[j];
                
                // mult (DONE)
                curHash[j] *= mf;
                curHash[j] %= mod[j];
                
                // add
                for (Integer x : adj[i]) {
                    int y = x;
                    if (x < i) {
                        y += n;
                    }
                    curHash[j] += (y - i);
                }
                curHash[j] %= mod[j];
            }
            boolean okay = true;
            for (j = 0; j < 2; j++)
                if (oldHash[j] != curHash[j])
                    okay = false;
            if (okay) {
                System.out.println("Yes");
                return;
            }
        }
        System.out.println("No");
    }
    
    public static int gcd(int a, int b) {
        return (b == 0) ? a : gcd(b, a % b);
    }
    public static class FS {
        BufferedReader br;
        StringTokenizer st;
        FS(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
            st = new StringTokenizer("");
        }
        String next() throws Exception {
            if (st.hasMoreTokens())
                return st.nextToken();
            st = new StringTokenizer(br.readLine());
            return next();
        }
        int nextInt() throws Exception {
            return Integer.parseInt(next());
        }
    }
}
