#include "game.h"
#include <bits/stdc++.h>
using namespace std;
#define FOR(i,a,b) for(int i=int(a);i<int(b);i++)
#define REP(i,b) FOR(i,0,b)
using vi=vector<int>;
#define PB push_back
const int Nmax=300010;
vi g[Nmax][2];
int n,k;
int reach[Nmax][2];
void init(int N, int K){
n=N+2;
k=K+2;
REP(i,k)REP(t,2)
reach[i][t]=i;
FOR(i,k,n){
reach[i][0]=0;
reach[i][1]=k-1;
}
}
bool dfs(int u,int v,int t){
if(v<k)return false;
int pre=reach[v][t];
reach[v][t]=(t==0?(const int&(*)(const int&,const int&))max<int>:(const int&(*)(const int&,const int&))min<int>)(reach[v][t],reach[u][t]);
if(reach[v][1]<=reach[v][0])return true;
int x=pre^reach[v][t^1];
int y=reach[v][t]^reach[v][t^1];
if(__builtin_clz(x)<__builtin_clz(y))
REP(s,2)
for(auto to:g[v][s])
if(dfs(v,to,s)) return true;
return false;
}
int add_teleporter(int u, int v){
if(u<k-2)u++;
else u+=2;
if(v<k-2)v++;
else v+=2;
if(max(u,v)<k){
if(u<v)return 0;
else return 1;
}
g[u][0].PB(v);
g[v][1].PB(u);
if(dfs(u,v,0))return 1;
if(dfs(v,u,1))return 1;
return 0;
}
