#include "overtaking.h"
#include <bits/stdc++.h>
using namespace std;
template<typename T>
using min_heap = priority_queue<T, vector<T>, greater<T>>;
template<typename T>
using max_heap = priority_queue<T, vector<T>, less<T>>;
using int64 = long long;
using ld = long double;
constexpr int kInf = 1e9 + 10;
constexpr int64 kInf64 = 1e15 + 10;
constexpr int kMod = 1e9 + 7;
struct Bus {
int index;
int64 depart; //the time taken by the bus to reach a checkpoint (aka the time it departs).
int64 time; //the fastest time taken by the bus to travel 1km.
bool operator<(const Bus &other) const {
return (depart != other.depart ? depart < other.depart : time < other.time);
}
};
struct Checkpoint {
int stop; //distance from the airport
vector<Bus> order; //order of buses coming into the checkpoint
};
int kLength;
int kBuses;
vector<Bus> buses;
int kCheckpoints;
vector<Checkpoint> checkpoints;
vector<vector<int>> position;
int64 kTime;
void init(int L, int N, vector<int64> T, vector<int> W, int X, int M, vector<int> S) {
kLength = L;
kTime = X;
for (int i = 0, j = 0; i < N; i++) {
if (W[i] <= X) continue;
buses.push_back({j,T[i], W[i]});
j++;
}
kBuses = buses.size();
kCheckpoints = M;
for (int i = 0; i < kCheckpoints; i++) {
checkpoints.push_back({S[i]});
}
assert(checkpoints[0].stop == 0);
for (int i = 0; i < kBuses; i++) {
checkpoints[0].order.push_back(buses[i]);
}
sort(checkpoints[0].order.begin(), checkpoints[0].order.end());
for (int i = 1; i < kCheckpoints; i++) {
const int64 dist = checkpoints[i].stop - checkpoints[i - 1].stop;
int64 prev = 0;
for (const Bus &bus : checkpoints[i - 1].order) {
const int64 reach = max(prev, dist * bus.time + bus.depart);
checkpoints[i].order.push_back({bus.index, reach, bus.time});
prev = reach;
}
sort(checkpoints[i].order.begin(), checkpoints[i].order.end());
}
position = vector<vector<int>>(kBuses, vector<int>(kCheckpoints));
for (int i = 0; i < kCheckpoints; i++) {
const vector<Bus> &order = checkpoints[i].order;
for (int j = 0; j < kBuses; j++) {
position[order[j].index][i] = j;
}
}
// for (const Checkpoint &checkpoint : checkpoints) {
// cout << checkpoint.stop << ":";
// for (const Bus &bus : checkpoint.order) {
// cout << " (" << bus.depart << ", " << bus.time << ")";
// }
// cout << '\n';
// }
}
int binary_search(const vector<Bus> &order, const int64 time) {
int lo = 0, hi = kBuses;
while (lo < hi) {
const int mid = (lo + hi) / 2;
if (order[mid].depart >= time) {
hi = mid;
} else {
lo = mid + 1;
}
}
return lo;
}
int64 arrival_time(int64 Y) {
int64 ans = Y;
for (int i = 0; i < kCheckpoints - 1; i++) {
const int dist = checkpoints[i + 1].stop - checkpoints[i].stop;
const Checkpoint &checkpoint = checkpoints[i];
int j = binary_search(checkpoint.order, ans);
ans += dist * kTime;
if (j != 0) {
const int k = position[checkpoint.order[j - 1].index][i + 1];
ans = max(ans, checkpoints[i + 1].order[k].depart);
}
}
return ans;
}
