// time_limit/sol_na_slower1.cpp
#include "overtaking.h"
#include <algorithm>
#include <numeric>
#include <iostream>
#include <cassert>
#include <array>
#include <map>
#define xx first
#define yy second
using namespace std;
using ll = long long;
int L, N, X, M;
vector<long long> T;
vector<int> W, S;
vector<vector<long long>> tm;
vector<vector<int>> ord;
pair<long long, int> get(long long Y);
vector<array<long long, 3>> lst;
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);
for (int j = 0; j < N; ++j)
ord[0].push_back(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];
}
for (int j = 0; j < N; ++j)
ord[i].push_back(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;
}
map<long long, pair<long long, int>> dp;
pair<long long, int> get(long long Y)
{
if (dp.count(Y))
return dp[Y];
ll prev = Y;
int sum = 0;
for (int i = 1; i < M; ++i)
{
int x = -1;
for (int j = 10; j >= 0; j--)
{
int xx = x + (1 << j);
if (xx < N && tm[i - 1][ord[i - 1][xx]] < prev)
x = xx;
}
ll res = prev + ll(S[i] - S[i - 1]) * X;
if (x != -1)
res = max(res, tm[i][ord[i - 1][x]]);
sum += x;
prev = res;
}
return dp[Y] = {prev, sum};
}
ll solve(ll L, ll R, ll Y)
{
if (L == R)
return get(Y).xx;
if (get(L).xx == get(R).xx)
return get(L).xx;
if (get(L).yy == get(R).yy && get(L).xx + R - L == get(R).xx)
return get(L).xx + Y - L;
ll mid = (L + R) >> 1;
return (Y <= mid ? solve(L, mid, Y) : solve(mid + 1, R, Y));
}
long long arrival_time(long long Y)
{
return solve(0, 1000'000'000'000'000'000LL, Y);
}
