// time_limit/sol_db_tle4.cpp
#include "overtaking.h"
#include <bits/stdc++.h>
#define all(x) (x).begin(), (x).end()
#define lsb(x) (x) & (-x)
using namespace std;
const int maxN = 1001;
typedef long long ll;
int n, m, x, ord[maxN][maxN];
ll arrive[maxN][maxN], premax[maxN][maxN], mem[maxN][maxN];
vector <int> ind, w, s;
vector <ll> t, sortedT[maxN];
int nextj[maxN][maxN];
void init(int L, int N, std::vector<long long> T, std::vector<int> W, int X, int M, std::vector<int> S)
{
n = N, m = M, x = X, t = sortedT[0] = T, w = W, s = S;
vector <int> inds;
for (int i = 0; i < N; ++i) {
arrive[0][i] = T[i];
inds.push_back(i);
}
auto order_buses = [&](int j) {
sort(all(inds), [&](int x, int y) {
return arrive[j][x] < arrive[j][y];
});
for (int i = 0; i < N; ++i) {
ord[j][i] = inds[i];
}
};
for (int j = 1; j < M; ++j) {
ll pre = 0, lpre = 0;
order_buses(j - 1);
for (int i = 0; i < N; ++i) {
if (i && arrive[j - 1][inds[i]] != arrive[j - 1][inds[i - 1]]) {
lpre = pre;
}
arrive[j][inds[i]] = max(arrive[j - 1][inds[i]] + 1ll * W[inds[i]] * (S[j] - S[j - 1]), lpre);
premax[j][i] = pre = max(pre, arrive[j][inds[i]]);
sortedT[j].push_back(arrive[j][inds[i]]);
}
}
order_buses(M - 1);
memset(mem, -1, sizeof mem);
}
ll calc(int j, ll y) {
if (j == m - 1) {
return y;
}
int index = lower_bound(all(sortedT[j]), y) - sortedT[j].begin();
if (index < n && sortedT[j][index] == y && mem[j][index] != -1) {
return mem[j][index];
}
int l = 0;
int r = n;
while (l < r) {
int q = l + r >> 1;
if (arrive[j][ord[j][q]] < y) {
l = q + 1;
} else {
r = q;
}
}
int nxtj = j + 1;
ll curt = y;
nxtj = max(nxtj, nextj[j][l]);
while (nxtj > j + 1 && (l? premax[nxtj][l - 1]: 0) >= y + 1ll * x * (s[nxtj] - s[j])) {
nxtj--;
}
ll res;
while (nxtj < m) {
curt = max(y + 1ll * x * (s[nxtj] - s[j]), l? premax[nxtj][l - 1]: 0);
if (curt == (l? premax[nxtj][l - 1]: 0)) {
nextj[j][l] = nxtj;
res = calc(nxtj, curt);
break;
}
nxtj++;
}
if (nxtj == m) {
res = curt;
}
nextj[j][l] = min(m - 1, nxtj);
if (index < n && sortedT[j][index] == y) {
mem[j][index] = res;
}
return res;
}
long long arrival_time(long long y)
{
return calc(0, y);
}
