#include "overtaking.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
ll l, x;
int n, m;
vector<ll> s;
vector<vector<tuple<ll, ll, int>>> table;
vector<vector<ll>> et;
vector<vector<ll>> dp;
void init(int L, int N, vector<ll> T, vector<int> W, int X, int M, vector<int> S) {
l = L, x = X;
m = M;
s.assign(S.begin(), S.end());
table.resize(m, vector<tuple<ll, ll, int>>(0));
for (int i = 0; i < N; i++) {
if (W[i] <= x) continue;
table[0].emplace_back(T[i], W[i], table[0].size());
}
n = table[0].size();
et.resize(m, vector<ll>(n));
for (int i = 0; i < n; i++) {
et[0][i] = get<0>(table[0][i]);
}
for (int i = 1; i < m; i++) {
sort(table[i - 1].begin(), table[i - 1].end());
table[i] = table[i - 1];
for (int j = 0; j < n; j++) {
auto &[t_nxt, w, idx] = table[i][j];
t_nxt = et[i - 1][idx] + w * (s[i] - s[i - 1]);
if (j) t_nxt = max(t_nxt, get<0>(table[i][j - 1]));
et[i][idx] = get<0>(table[i][j]);
}
}
dp.resize(m, vector<ll>(n, -1));
return;
}
void update(vector<pair<int, int>> &dp_empty, ll arrive) {
for (auto [i, k] : dp_empty) {
dp[i][k] = arrive;
}
}
ll arrival_time(ll Y) {
vector<pair<int, int>> dp_empty;
ll start = Y, arrive = 0;
if (start + x * (s[m - 1] - s[0]) > get<0>(table[m - 1].back())) {
return start + x * (s[m - 1] - s[0]);
}
for (int i = 1; i < m; i++) {
arrive = start + x * (s[i] - s[i - 1]);
auto itr = lower_bound(table[i - 1].begin(), table[i - 1].end(), make_tuple(start, x, n + 1));
if (itr == table[i - 1].begin()) {
arrive = start + x * (s[m - 1] - s[i - 1]);
break;
} else {
itr = prev(itr);
int k = itr - table[i - 1].begin();
if (dp[i][k] != -1) {
arrive = dp[i][k];
break;
}
dp_empty.emplace_back(i, k);
auto [_, __, j] = *itr;
arrive = max(arrive, et[i][j]);
}
start = arrive;
}
update(dp_empty, arrive);
return arrive;
}
