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.*;

public class Main {
  static Scanner in = new Scanner(System.in);
  static PrintWriter out = new PrintWriter(System.out);

  static int gcd (int a, int b) {
    if (b == 0) return a;
    return gcd(b, a % b);
  }
  
  public static void main(String[] args) {
    int n = in.nextInt();
    int m = in.nextInt();

    int[][] segments = new int[m][2];
    HashSet<Long> hash_segments = new HashSet<>();
    for (int i = 0; i < m; i++) {
      int start_line = in.nextInt();
      int end_line = in.nextInt();
      segments[i][0] = Math.min(start_line, end_line);
      segments[i][1] = Math.max(start_line, end_line);
      hash_segments.add(((long)segments[i][0] << 32) | (long)segments[i][1]);
    }

    TreeSet<Integer> steps = new TreeSet<>();
    for (int i = 1; i < n; i++) {
      steps.add(gcd(i, n));
    }

    Iterator<Integer> it = steps.iterator();
    boolean match = true;
    while (it.hasNext()) {
      int k = it.next();
      for (int i = 0; i < m; i++) {
        int a = segments[i][0] + k;
        int b = segments[i][1] + k;
        if (a > n) a -= n;
        if (b > n) b -= n;
        long hash_ab = ((long)Math.min(a, b) << 32) | (long)Math.max(a, b);
        // out.println("min ab: " + Math.min(a, b) + " max ab: " + Math.max(a, b));
        // out.println("hash ab: " + hash_ab);
        if (hash_segments.contains(hash_ab)) {
          match = true;
        } else {
          match = false;
          break;
        }
        // out.println("shifted_seg start: " + shifted_segments[i][0] + " shifted_seg end: " + shifted_segments[i][1]);
        // int counter = 0;
        // boolean found = false;
        // while (counter < m) {
        //   if (Math.min(a, b) == segments[counter][0] &&
        //   Math.max(a, b) == segments[counter][1]) {
        //     found = true;
        //     break;
        //   }
        //   counter++;
        // }
        // if (!found) {
        //   match = false;
        //   break;
        // } else {
        //   match = true;
        // }
      }
      // out.println("k: " + k + (match ? " match" : " not match"));
      if (match) break;
    }

    if (match) {
      out.println("Yes");
    } else {
      out.println("No");
    }

    in.close();
    out.close();
  }
}