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 D implements Runnable {
	public static void main (String[] args) {new Thread(null, new D(), "_cf", 1 << 28).start();}
	
	public void run() {
		FastScanner fs = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);
		System.err.println("");

		int n = fs.nextInt();
		int m = fs.nextInt();
		ArrayList<Integer>[] deltas = new ArrayList[n];
		for(int i = 0; i < n; i++) deltas[i] = new ArrayList<Integer>();
		for(int i = 0; i < m; i++) {
			int u = fs.nextInt()-1;
			int v = fs.nextInt()-1;
			if(u < v) {
				deltas[u].add(v-u);
				deltas[v].add(n-v + u);
			}
			else {
				deltas[v].add(u-v);
				deltas[u].add(n-u + v);
			}
		}
		for(int i = 0; i < n; i++) Collections.sort(deltas[i]);
		StringBuilder sb = new StringBuilder();
		for(int i = 0; i < n; i++) {
			if(deltas[i].isEmpty()) {
				sb.append("#");
			}
			else {
				for(int x : deltas[i]) {
					sb.append("+").append(x);
				}
			}
			
			sb.append("$");
		}
		
		String pass = sb.toString() + sb.toString();
		int match = sb.length();
		int[] z = zValues(pass);
		boolean res = false;
		for(int i = 1; i < match; i++) {
			if(z[i] >= match) {
				res = true;
				break;
			}
		}
		if(res) out.println("Yes");
		else out.println("No");
		
		out.close();
	}
	
	public int[] zValues(String string) {
		int n = string.length();  char[] s = string.toCharArray();
		int[] z = new int[n];  z[0] = n;
		int L = 0, R = 0;
		int[] left = new int[n], right = new int[n];
		for(int i = 1; i < n; ++i) {
			if(i > R) {
				L = R = i;
				while(R < n && s[R-L] == s[R]) R++;
				z[i] = R - L;  R--;
			} else {
				int k = i-L;
				if(z[k] < R-i+1) z[i] = z[k];
				else {
					L = i;
					while(R < n && s[R-L] == s[R]) R++;
					z[i] = R - L;  R--;
				}
			}
			left[i] = L;  right[i] = R;
		}
		return z;
	}
	
	class FastScanner {
		public int BS = 1<<16;
		public char NC = (char)0;
		byte[] buf = new byte[BS];
		int bId = 0, size = 0;
		char c = NC;
		double num = 1;
		BufferedInputStream in;

		public FastScanner() {
			in = new BufferedInputStream(System.in, BS);
		}

		public FastScanner(String s) throws FileNotFoundException {
			in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
		}

		public char nextChar(){
			while(bId==size) {
				try {
					size = in.read(buf);
				}catch(Exception e) {
					return NC;
				}                
				if(size==-1)return NC;
				bId=0;
			}
			return (char)buf[bId++];
		}

		public int nextInt() {
			return (int)nextLong();
		}

		public long nextLong() {
			num=1;
			boolean neg = false;
			if(c==NC)c=nextChar();
			for(;(c<'0' || c>'9'); c = nextChar()) {
				if(c=='-')neg=true;
			}
			long res = 0;
			for(; c>='0' && c <='9'; c=nextChar()) {
				res = (res<<3)+(res<<1)+c-'0';
				num*=10;
			}
			return neg?-res:res;
		}

		public double nextDouble() {
			double cur = nextLong();
			return c!='.' ? cur:cur+nextLong()/num;
		}

		public String next() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c>32) {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public String nextLine() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c!='\n') {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public boolean hasNext() {
			if(c>32)return true;
			while(true) {
				c=nextChar();
				if(c==NC)return false;
				else if(c>32)return true;
			}
		}
		
		public int[] nextIntArray(int n) {
			int[] res = new int[n];
			for(int i = 0; i < n; i++) res[i] = nextInt();
			return res;
		}
		
	}

	
}