#include "game.h"
#include <bits/stdc++.h>
int n, k;
constexpr int N = 3e5 + 5;
int lb[N], rb[N];
std::vector<int> adj[N];
std::vector<int> radj[N];
void add_edge(int u, int v) {
adj[u].push_back(v);
radj[v].push_back(u);
}
void init(int _n, int _k) {
n = _n + 1;
k = _k;
for (int i = 1; i <= n; i++) {
lb[i] = 0;
rb[i] = k + 1;
}
for (int i = 1; i <= k; i++) {
lb[i] = i;
rb[i] = i;
}
for (int i = 1; i + 1 <= k; i++) {
add_edge(i, i + 1);
}
}
bool update_edge(int, int);
bool update_vertex(int u) {
for (int v : adj[u]) {
if (update_edge(u, v)) return true;
}
for (int v : radj[u]) {
if (update_edge(v, u)) return true;
}
return false;
}
bool update_edge(int u, int v) {
int be_reached_min_u = lb[u];
int be_reached_max_u = u <= k ? rb[u] : rb[u] - 1;
int can_reach_min_v = v <= k ? lb[v] : lb[v] + 1;
int can_reach_max_v = rb[v];
// std::cerr << u << " " << v << std::endl;
// std::cerr << be_reached_min_u << " " << be_reached_max_u << " " << can_reach_max_v << " " << can_reach_min_v << std::endl;
if (be_reached_min_u >= can_reach_max_v) {
return true;
}
if (be_reached_max_u < can_reach_min_v) {
return false;
}
if ((lb[v] + rb[v]) / 2 + 1 <= be_reached_min_u) {
// we can shift it to the right
int m = (lb[v] + rb[v]) / 2;
while (m + 1 <= be_reached_min_u) {
lb[v] = m + 1;
m = (lb[v] + rb[v]) / 2;
}
if (update_vertex(v)) return true;
}
if ((lb[u] + rb[u]) / 2 >= can_reach_max_v) {
int m = (lb[u] + rb[u]) / 2;
while (m >= can_reach_max_v) {
rb[u] = m;
m = (lb[u] + rb[u]) / 2;
}
if (update_vertex(u)) return true;
}
return false;
}
int add_teleporter(int u, int v) {
u++, v++;
if (u == v) {
if (u <= k) {
return 1;
}
return 0;
}
if (v <= u && u <= k) { // eliminates
return 1;
}
add_edge(u, v);
return update_edge(u, v);
}
