#include "game.h"
#include <bits/stdc++.h>
#define forf(i,a,b) for(int i = a; i<=b; i++)
#define forb(i,b,a) for(int i = b; i>=a; i--)
using namespace std;
int N,K;
int S[1000001][21];
vector<int> adj[1000001],radj[1000001];
void dnc(int dep, int s, int e){
if(s>e) return;
int m = s+e>>1;
forf(i,2*s,2*m) S[i][dep] = 1;
forf(i,2*m+1,2*e+1) S[i][dep] = 2;
dnc(dep+1,s,m-1), dnc(dep+1,m+1,e);
}
void forward(int now){
for(auto i : adj[now]){
int p = 0;
while(p<20 && S[now][p] == S[i][p]) p++;
if((S[now][p]&2) && S[i][p] == 0) S[i][p] = 2, forward(i);
assert(!((S[now][p]&2) && (S[i][p]&1)));
}
}
void backward(int now){
for(auto i : radj[now]){
int p = 0;
while(p<20 && S[now][p] == S[i][p]) p++;
if((S[now][p]&1) && S[i][p] == 0) S[i][p] = 1, backward(i);
assert(!((S[now][p]&1) && (S[i][p]&2)));
}
}
void init(int n, int k){
N =n, K=k;
dnc(0,0,k-1);
forf(i,0,2*k-2) adj[i].push_back(i+1), radj[i+1].push_back(i);
}
int add_teleporter(int u, int v) {
if(u < K) u = 2*u+1;
else u += 2*K;
if(v < K) v = 2*v;
else v += 2*K;
int p = 0;
while(p<20 && (S[u][p] == S[v][p])) p++;
if((S[u][p]&2) && (S[v][p]&1)) return 1;
adj[u].push_back(v); radj[v].push_back(u);
forf(i,0,20) forward(u), backward(v);
return 0;
}
