#include "Alicelib.h"
#include <cassert>
#include <cstdio>
#include <bits/stdc++.h>
using namespace std;
#define dbgv(v) cout<<#v<<" = "; f(i,0,v.size()) cout<<v[i]<<" "; cout<<endl
#define dbga(a,x,y) cout<<#a<<" = "; f(i,x,y) cout<<a[i]<<" "; cout<<endl
#define erorp(x) cout<<#x<<"={"<<x.F<<" , "<<x.S<<"}"<<endl
#define eror(x) cout<<#x<<'='<<(x)<<endl
#define f_(i,a,b) for(int i=a;i>=b;i--)
#define f(i,a,b) for(int i=a;i<b;i++)
#define nb(x) __builtin_popcount(x)
#define all(v) v.begin(),v.end()
#define bit(n,k) (((n)>>(k))&1)
#define Add(x,y) x=(x+y)%mod
#define maxm(a,b) a=max(a,b)
#define minm(a,b) a=min(a,b)
#define lst(x) x[x.size()-1]
#define sz(x) int(x.size())
#define mp make_pair
#define ll long long
#define pb push_back
#define S second
#define F first
const int N=1e6+99,lg=10;
int n,m,cnt;
vector<pair<int,int>> edge;
void Alice(int _n,int _m,int A[],int B[] ){
n=_n,m=_m;
f(i,0,n){
f(j,0,lg){
if(bit(i+1,j)){
edge.pb({i,n+j});
}
}
}
f(j,0,lg-1) edge.pb({n+j,n+j+1});
f(i,0,n+lg) edge.pb({i,n+lg});
f(i,n,n+lg) edge.pb({i,n+lg+1});
InitG(n+lg+2,m+edge.size());
f(i,0,m) MakeG(cnt++,A[i],B[i]);
for(auto p : edge) MakeG(cnt++,p.F,p.S);
}
/*void Alice( int N, int M, int A[], int B[] ){
InitG(3,2);
MakeG(0,0,1);
MakeG(1,1,2);
}*/
#include "Boblib.h"
#include <cassert>
#include <cstdio>
#include <bits/stdc++.h>
using namespace std;
#define dbgv(v) cout<<#v<<" = "; f(i,0,v.size()) cout<<v[i]<<" "; cout<<endl
#define dbga(a,x,y) cout<<#a<<" = "; f(i,x,y) cout<<a[i]<<" "; cout<<endl
#define erorp(x) cout<<#x<<"={"<<x.F<<" , "<<x.S<<"}"<<endl
#define eror(x) cout<<#x<<'='<<(x)<<endl
#define f_(i,a,b) for(int i=a;i>=b;i--)
#define f(i,a,b) for(int i=a;i<b;i++)
#define nb(x) __builtin_popcount(x)
#define all(v) v.begin(),v.end()
#define bit(n,k) (((n)>>(k))&1)
#define Add(x,y) x=(x+y)%mod
#define maxm(a,b) a=max(a,b)
#define minm(a,b) a=min(a,b)
#define lst(x) x[x.size()-1]
#define sz(x) int(x.size())
#define mp make_pair
#define ll long long
#define pb push_back
#define S second
#define F first
const int N=1111;
int g[N][N],deg[N],mark[N],ans[N];
void Bob(int n, int m,int A[],int B[]){
/*cout<<n<<" - "<<m<<endl;
f(i,0,m){
cout<<A[i]<<" "<<B[i]<<endl;
}*/
int x=0;
f(i,0,m) deg[A[i]]++,deg[B[i]]++,g[A[i]][B[i]]=g[B[i]][A[i]]=1;
f(i,0,n){
if(deg[i]>deg[x]) x=i;
}
ans[x]=-1;
f(i,0,n){
if(i!=x && g[i][x]==0){
x=i;
break ;
}
}
ans[x]=-1;
vector<int> vec;
f(i,0,n){
if(g[x][i]==1){
ans[i]=-1;
mark[i]=1;
}
}
f(i,0,n){
if(mark[i]){
int deg=0;
f(j,0,n){
if(mark[j] && g[i][j]){
deg++;
}
}
if(deg==1){
x=i;
break ;
}
}
}
for(int u=x,b=1;b;){
mark[u]=b=0;
vec.pb(u);
f(i,0,n) if(g[u][i] && mark[i]){
u=i,b=1;
break ;
}
}
int deg0=0,deg1=0;
f(i,0,n){
deg0+=g[vec[0]][i];
deg1+=g[vec.back()][i];
}
if(deg0<deg1){
reverse(all(vec));
}
vector<pair<int,int>> edge;
f(i,0,n){
if(ans[i]==-1) continue ;
f(j,0,vec.size()) ans[i]^=g[i][vec[j]]*(1<<j);
}
f(i,0,m){
if(ans[A[i]]>0 && ans[B[i]]>0){
edge.pb({ans[A[i]]-1,ans[B[i]]-1});
}
}
InitMap(n-12,edge.size());
for(auto p : edge){
MakeMap(p.F,p.S);
}
}
