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.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

public class Main {
	public static int N, M;
	public static segment[] orig, now;

	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		N = s.nextInt();
		M = s.nextInt();
		orig = new segment[M];
		now = new segment[M];
		for (int i = 0; i < M; i++) {
			int a = s.nextInt() - 1;
			int b = s.nextInt() - 1;
			orig[i] = new segment(a, b);
		}
		Arrays.sort(orig);
		ArrayList<Integer> factors = new ArrayList<Integer>();
		for (int i = 1; i < N; i++) {
			if (N % i == 0) {
				factors.add(i);
			}
		}
		for (int i : factors) {
			for (int k = 0; k < M; k++) {
				now[k] = new segment((orig[k].min + i) % N, (orig[k].max + i) % N);
			}
			if (check()) {
				System.out.println("Yes");
				return;
			}
		}
		System.out.println("No");
	}

	public static boolean check() {
		for (int i = 0; i < M; i++) {
			now[i].rearrange();
		}
		Arrays.sort(now);
		for (int i = 0; i < M; i++) {
			if (orig[i].min != now[i].min || orig[i].max != now[i].max) {
				return false;
			}
		}
		return true;
	}
}

class segment implements Comparable<segment> {
	public int min, max;

	public segment(int a, int b) {
		min = Math.min(a, b);
		max = Math.max(a, b);
	}

	public void rearrange() {
		if (min > max) {
			min = max ^ min ^ (max = min);
		}
	}

	public int compareTo(segment next) {
		if (min == next.min) {
			return max - next.max;
		}
		return min - next.min;
	}

	public String toString() {
		return min + " " + max;
	}
}
