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.*;

/******************************\
 * The solution is at the top *
 *                            *
 *   Created by : azhar556    *
\******************************/

public class Solution {
    static void solve() {
        int n = ni();
        int m = ni();
        NavigableSet<Integer>[] grEdge = new TreeSet[n + 1];
        for (int i = 0; i < n + 1; i++) {
            grEdge[i] = new TreeSet<Integer>();
        }
        for (int i = 0; i < m; i++) {
            int a = ni();
            int b = ni();
            if (a > b) {
                int sav = b;
                b = a;
                a = sav;
            }
            int jarakBiasa = b - a;
            int jarakTembus = n - b + a;
            grEdge[a].add(jarakBiasa);
            grEdge[b].add(jarakTembus);
        }
        /*for (int i = 1; i <= n; i++) {
            err.print(i + " > ");
            for (int x : grEdge[i]) err.print(x + " ");
            err.println();
        }*/
        // find pattern divisor
        NavigableSet<Integer> divisor = new TreeSet<>();
        for (int i = 1; i <= n / 2; i++) { // range
            if (n % i != 0) continue;
            boolean gotcha = true;
            for (int j = i; j < n; j += i) { // now coordinat
                if (!grEdge[n].equals(grEdge[j])) {
                    gotcha = false;
                    break;
                }
            }
            if (gotcha) {
                divisor.add(i); //err.print(i + " ");
            }
        }
        // transforming divisor..........
        if (divisor.size() == 0) {
            out.println("No"); return;
        }
        // checking result...
        while (divisor.size() > 0) {
            int nowDivisor = divisor.pollFirst();
            boolean yes = true;
            for (int i = 1; i < nowDivisor; i++) {
                for (int j = i; j < n; j += nowDivisor) {
                    if (!grEdge[i].equals(grEdge[j])) {
                        yes = false;
                        break;
                    }
                }    
            } 
            if (yes) {
                out.println("Yes"); return;
            }
        }
        out.println("No");         
    }    

    public static void main(String[] args) {
        long time = System.currentTimeMillis();
        int t;// = ni();
        t = 1;
        while (t-- > 0) solve(); 
        err.println("Time elapsed : " + (System.currentTimeMillis() - time) / 1000F + " s.");
        err.close(); out.close();
    }

    static PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
    static PrintWriter err = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.err)));
    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    static StringTokenizer token;
        
    static String ns() {
        while (token == null || !token.hasMoreTokens()) {
            try {
                token = new StringTokenizer(br.readLine());
            }
            catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return token.nextToken();
    }
    static char nc() {
        return Character.valueOf(ns().charAt(0));
    }
    static int ni() {
        return Integer.parseInt(ns());
    }
    static double nd() {
        return Double.parseDouble(ns());
    }
    static long nl() {
        return Long.parseLong(ns());
    }
}
