Codeforces 1162D Chladni Figure（枚举因子）

//      ——By DD_BOND 

//#include<bits/stdc++.h>
#include<functional>
#include<algorithm>
#include<iostream>
#include<sstream>
#include<iomanip>
#include<climits>
#include<cstring>
#include<cstdlib>
#include<cstddef>
#include<cstdio>
#include<memory>
#include<vector>
#include<cctype>
#include<string>
#include<cmath>
#include<queue>
#include<deque>
#include<ctime>
#include<stack>
#include<map>
#include<set>

#define fi first
#define se second
#define MP make_pair
#define pb push_back
#define INF 0x3f3f3f3f
#define pi 3.1415926535898
#define lowbit(a)  (a&(-a))
#define lson l,(l+r)/2,rt<<1
#define rson (l+r)/2+1,r,rt<<1|1
#define Min(a,b,c)  min(a,min(b,c))
#define Max(a,b,c)  max(a,max(b,c))
#define debug(x)  cerr<<#x<<"="<<x<<"\n";

using namespace std;

typedef long long ll;
typedef pair<int,int> P;
typedef pair<ll,ll> Pll;
typedef unsigned long long ull;

const ll LLMAX=2e18;
const int MOD=1e9+7;
const double eps=1e-8;
const int MAXN=1e6+10;

inline ll sqr(ll x){ return x*x; }
inline int sqr(int x){ return x*x; }
inline double sqr(double x){ return x*x; }
ll gcd(ll a,ll b){ return b==0? a: __gcd(b,a%b); }
ll exgcd(ll a,ll b,ll &x,ll &y){ ll d; (b==0? (x=1,y=0,d=a): (d=exgcd(b,a%b,y,x),y-=a/b*x)); return d; }
ll qpow(ll a,ll n){ll sum=1;while(n){if(n&1)sum=sum*a%MOD;a=a*a%MOD;n>>=1;}return sum;}
inline int dcmp(double x){  if(fabs(x)<eps) return 0;   return (x>0? 1: -1); }

P que[MAXN];
int num[MAXN];
map<int,map<int,int> >mp;

int main(void)
{
    ios::sync_with_stdio(false);    cin.tie(0);   cout.tie(0);   
    int n,m,l,r,len;    cin>>n>>m;
    if(n==2)    return cout<<"YES"<<endl,0;
    for(int i=0;i<m;i++){
        cin>>l>>r;
        len=min((r-l+n)%n,n-(r-l+n)%n);
        mp[l][r]=mp[r][l]=1;
        num[len]++;
        que[i]=P(l,r);
    }
    for(int i=1;i*i<=num[len];i++){
        if(num[len]%i==0){
            if(i!=1&&n%i==0){
                int flag=0,d=n/i;
                for(int j=0;j<m;j++){
                    int l=que[j].fi,r=que[j].se,ld=l+d,rd=r+d;
                    if(ld>n)    ld-=n;  
                    if(rd>n)    rd-=n;
                    if(mp[ld].find(rd)==mp[ld].end()){
                        flag=1;
                        break;
                    }
                }
                if(!flag)   return cout<<"Yes"<<endl,0;
            }
            if(num[len]/i!=1&&n%(num[len]/i)==0){
                int flag=0,d=n/(num[len]/i);
                for(int j=0;j<m;j++){
                    int l=que[j].fi,r=que[j].se,ld=l+d,rd=r+d;
                    if(ld>n)    ld-=n;  
                    if(rd>n)    rd-=n;
                    if(mp[ld].find(rd)==mp[ld].end()){
                        flag=1;
                        break;
                    }
                }
                if(!flag)   return cout<<"Yes"<<endl,0;
            }
        }
    }
    cout<<"No"<<endl;
    return 0;
}