Codeforces Round #557 (Div. 2) D – Chladni Figure(分解素因子)

//#include<bits/stdc++.h>
#include<algorithm>
#include <iostream>
#include   <fstream>
#include  <cstdlib>
#include  <cstring>
#include  <cassert>
#include   <cstdio>
#include   <vector>
#include   <string>
#include    <cmath>
#include    <queue>
#include    <stack>
#include      <set>
#include      <map>
using namespace std;
#define P(a,b,c) make_pair(a,make_pair(b,c))
#define rep(i,a,n) for (int i=a;i<=n;i++)
#define per(i,a,n) for (int i=n;i>=a;i--)
#define CLR(vis) memset(vis,0,sizeof(vis))
#define MST(vis,pos) memset(vis,pos,sizeof(vis))
#define pb push_back
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
#define SZ(x) ((int)(x).size())
typedef pair<int,pair<int,int> >pii;
typedef long long ll;
typedef unsigned long long ull;
const ll mod = 1000000007;
const int INF = 0x3f3f3f3f;
ll gcd(ll a, ll b) {
	return b ? gcd(b, a%b) : a;
}
template<class T>inline void gmax(T &A, T B) {
	(A<B)&&(A=B);//if(B>A)A=B;
}
template<class T>inline void gmin(T &A, T B) {
	(A>B)&&(A=B);//if(B<A)A=B;
}
template <class T>
inline bool scan_d(T &ret) {
	char c;
	int sgn;
	if(c=getchar(),c==EOF) return 0; //EOF
	while(c!='-'&&(c<'0'||c>'9')) c=getchar();
	sgn=(c=='-')?-1:1;
	ret=(c=='-')?0:(c-'0');
	while(c=getchar(),c>='0'&&c<='9') ret=ret*10+(c-'0');
	ret*=sgn;
	return 1;
}
inline void outt(int x) {
	if(x>9) outt(x/10);
	putchar(x%10+'0');
}
const int MAXN = 1e6+10;
ll x[MAXN];
ll y[MAXN];
map<ll,int>vis;
int fac[100];
int main() {
	ll n,m;
	cin>>n>>m;
	rep(i,1,m){
		scan_d(x[i]);
		scan_d(y[i]);
		vis[x[i]*1000000+y[i]]=1;
	}
	int N=n;
	int cnt=0;
	for(int i=2;i<=sqrt(N);i++){
		if(N%i==0)fac[++cnt]=i;
		while(N%i==0)N/=i;
	}
	if(N>1)fac[++cnt]=N;
	int flag1,flag2;
	flag1=0;
	rep(i,1,cnt){
		flag2=1;
		rep(j,1,m){
			ll X=(x[j]+n/fac[i]);
			ll Y=(y[j]+n/fac[i]);
			if(X>n)X-=n;
			if(Y>n)Y-=n;
			if(!vis[X*1000000+Y]&&!vis[Y*1000000+X]){
				flag2=0;
				break;
			}
		}
		if(flag2){
			flag1=1;
			break;
		}
	}
	if(flag1)puts("Yes");
	else puts("No");
	return 0;
}