// correct/sol_na_full.cpp
#include "overtaking.h"
#include <algorithm>
#include <numeric>
#include <iostream>
#include <cassert>
#include <array>
#include <map>
#include <unordered_map>
#define xx first
#define yy second
using namespace std;
using ll = long long;
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
int L, N, X, M;
vector<long long> T;
vector<int> W, S;
vector<vector<long long>> tm;
vector<vector<int>> ord;
void init(int L_, int N_, std::vector<long long> T_, std::vector<int> W_, int X_, int M_, std::vector<int> S_)
{
L = L_;
N = N_;
T = T_;
W = W_;
X = X_;
M = M_;
S = S_;
tm.assign(M, vector<long long>(N));
for (int i = 0; i < N; ++i)
{
tm[0][i] = T[i];
}
ord.resize(M);
ord[0].resize(N);
for (int j = 0; j < N; ++j)
ord[0][j] = j;
sort(ord[0].begin(), ord[0].end(), [&](int x, int y) -> bool
{
if(tm[0][x]==tm[0][y]) return W[x]<W[y];
return tm[0][x]<tm[0][y]; });
for (int i = 1; i < M; ++i)
{
vector<array<ll, 3>> lst; //{start, en, ind}
for (int j = 0; j < N; ++j)
{
lst.push_back({tm[i - 1][j], tm[i - 1][j] + (ll)W[j] * ll(S[i] - S[i - 1]), j});
}
sort(lst.begin(), lst.end(), [&](auto &x, auto &y) -> bool
{
if(x[0]==y[0]) return W[x[2]]>W[y[2]];
return x[0]<y[0]; });
ll prev = 0;
for (int j = 0; j < N;)
{
int k;
ll curr = 0;
for (k = j; k < N && lst[j][0] == lst[k][0]; k++)
{
lst[k][1] = max(lst[k][1], prev);
curr = max(curr, lst[k][1]);
}
prev = max(curr, prev);
j = k;
}
for (int j = 0; j < N; ++j)
{
tm[i][lst[j][2]] = lst[j][1];
}
ord[i].resize(N);
for (int j = 0; j < N; ++j)
ord[i][j] = j;
sort(ord[i].begin(), ord[i].end(), [&](int x, int y) -> bool
{
if(tm[i][x]==tm[i][y]) return W[x]<W[y];
return tm[i][x]<tm[i][y]; });
}
return;
}
#include <ext/pb_ds/assoc_container.hpp>
__gnu_pbds::gp_hash_table<ll, ll> dp[1001];
vector<pair<ll, ll>> poss;
long long get(long long Y)
{
ll prev = Y;
poss.clear();
for (int i = 1; i < M; ++i)
{
int x = -1;
if (tm[i - 1][ord[i - 1][0]] < prev)
{
int L = -1, R = N - 1;
while (L < R)
{
int mid = (L + R + 1) / 2;
if (tm[i - 1][ord[i - 1][mid]] < prev)
L = mid;
else
R = mid - 1;
}
x = L;
}
ll res = prev + ll(S[i] - S[i - 1]) * X;
if (x != -1)
{
if (res <= tm[i][ord[i - 1][x]])
{
res = max(res, tm[i][ord[i - 1][x]]);
auto it = dp[i].find(res);
if (it != dp[i].end())
{
prev = it->yy;
break;
}
prev = res;
poss.push_back({i, res});
continue;
}
else
{
int L = i, R = M - 1;
while (L < R)
{
int mid = (L + R + 1) / 2;
if (tm[mid][ord[mid - 1][x]] < prev + ll(S[mid] - S[i - 1]) * X)
L = mid;
else
R = mid - 1;
}
int to = L;
prev = prev + ll(S[to] - S[i - 1]) * X;
i = to;
continue;
}
}
else
{
int L = i, R = M - 1;
while (L < R)
{
int mid = (L + R + 1) / 2;
if (tm[mid - 1][ord[mid - 1][0]] >= prev + ll(S[mid] - S[i - 1]) * X)
L = mid;
else
R = mid - 1;
}
int to = L;
prev = prev + ll(S[to] - S[i - 1]) * X;
i = to;
continue;
}
}
for (auto &i : poss)
{
dp[i.xx][i.yy] = prev;
}
return prev;
}
long long arrival_time(long long Y)
{
return get(Y);
}
