#include "game.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
#define MASK(i) (1ULL << (i))
#define GETBIT(mask, i) (((mask) >> (i)) & 1)
#define ALL(v) (v).begin(), (v).end()
ll max(ll a, ll b){return (a > b) ? a : b;}
ll min(ll a, ll b){return (a < b) ? a : b;}
ll gcd(ll a, ll b){return __gcd(abs(a), abs(b));}
ll lcm(ll a, ll b){return abs(a) / gcd(a, b) * abs(b);}
ll LASTBIT(ll mask){return (mask) & (-mask);}
int pop_cnt(ull mask){return __builtin_popcountll(mask);}
int ctz(ull mask){return __builtin_ctzll(mask);}
int logOf(ull mask){return 63 - __builtin_clzll(mask);}
// mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
mt19937_64 rng(1);
ll rngesus(ll l, ll r){return l + (ull) rng() % (r - l + 1);}
double rngesus_d(double l, double r){
double cur = rngesus(0, MASK(60) - 1);
cur /= MASK(60) - 1;
return l + cur * (r - l);
}
template <class T1, class T2>
bool maximize(T1 &a, T2 b){
if (a < b) {a = b; return true;}
return false;
}
template <class T1, class T2>
bool minimize(T1 &a, T2 b){
if (a > b) {a = b; return true;}
return false;
}
template <class T>
void printArr(T container, string separator = " ", string finish = "\n", ostream &out = cout){
for(auto item: container) out << item << separator;
out << finish;
}
template <class T>
void remove_dup(vector<T> &a){
sort(ALL(a));
a.resize(unique(ALL(a)) - a.begin());
}
const int N = 3e5 + 69, LOG_N = 19;
int n, k;
vector<int> graph[N], rgraph[N];
pair<int, int> range[N];
int level[N];
void init(int _n, int _k) {
n = _n, k = _k;
for(int i = 1; i <= n; ++i) {
range[i] = {n+1, 0};
level[i] = LOG_N - 1;
}
for(int i = 1; i <= k; ++i){
range[i] = {i, i-1};
}
}
int check_vertex(int x);
int add_edge(int u, int v){
int val1 = range[u].second, val2 = range[v].first;
if (u <= k) val1 = u;
if (v <= k) val2 = v;
maximize(range[v].second, val1);
minimize(range[u].first, val2);
if (range[u].first <= range[u].second) return 1;
if (range[v].first <= range[v].second) return 1;
bool check1 = false, check2 = false;
while (GETBIT(range[u].first, level[u]) == GETBIT(range[u].second, level[u])){
check1 = true;
level[u]--;
}
while (GETBIT(range[v].first, level[v]) == GETBIT(range[v].second, level[v])){
check2 = true;
level[v]--;
}
if (check1){
if (check_vertex(u)) return 1;
}
if (check2){
if (check_vertex(v)) return 1;
}
return 0;
}
int check_vertex(int u){
for(int v: graph[u]) if (add_edge(u, v)) return 1;
for(int v: rgraph[u]) if (add_edge(v, u)) return 1;
return 0;
}
int add_teleporter(int u, int v) {
u++; v++;
if (u <= k && v <= k){
if (u >= v) return 1;
return 0;
}
graph[u].push_back(v);
rgraph[v].push_back(u);
return add_edge(u, v);
}
