#include "overtaking.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const ll inf = 2e18;
ll tn;
ll l, n, m;
vector<int> stations;
struct Line{
ll a, b, id; Line( ll a = 0, ll b = 0, ll id = 0 ) : a(a), b(b), id(id) {}
bool operator < ( Line l ){
if( b == l.b ) return a > l.a;
return b > l.b;
}
ll calc( ll x ){ return a*x + b; }
};
vector<Line> bus;
vector<set<pair<ll, ll>>> s;
void init(int L, int N, vector<ll> T, vector<int> W, int X, int M, vector<int> S)
{
tn = X;
l = L;
n = N;
m = M;
s.resize(m);
for( int i = 0; i < n; i++ ) bus.push_back(Line( W[i], T[i], i ));
stations = S;
vector<vector<int>> adj(n);
vector<ll> t(n), marc(n);
vector<Line> lines;
for( auto x : bus ) lines.push_back(x);
function<void(int, ll)> dfs = [&]( int cur, ll val ){
t[cur] = val;
marc[cur] = true;
for( int viz : adj[cur] ) dfs( viz, val );
};
for( int pos = 1; pos < (int)stations.size(); pos++ ){
fill( marc.begin(), marc.end(), 0);
sort( lines.begin(), lines.end() );
adj.clear();
adj.resize(n);
stack<pair<ll, int>> pilha;
ll delta = stations[pos] - stations[pos - 1];
for( auto x : lines ){
t[x.id] = x.calc(delta);
while( !pilha.empty() && pilha.top().first <= t[x.id] ){
adj[x.id].push_back(pilha.top().second );
pilha.pop();
}
pilha.push({ t[x.id], x.id });
}
reverse( lines.begin(), lines.end() );
for( auto x : lines ){
if( !marc[x.id] ) dfs( x.id, t[x.id] );
s[pos - 1].insert({ x.b, t[x.id] });
}
s[pos - 1].insert({ -inf, -inf });
lines.clear();
for( auto x : bus ) lines.push_back(Line(x.a, t[x.id], x.id));
}
}
ll arrival_time(ll y){
for( int i = 0; i + 1 < (int)stations.size(); i++ ){
auto [antes, depois] = *prev(s[i].lower_bound({ y, -inf }));
ll delta = stations[i + 1] - stations[i];
y = max( y + delta*tn, depois );
}
return y;
}
