#include "overtaking.h"
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ll long long
#define ld long double
#define ull unsigned long long
#define ff first
#define ss second
#define pii pair<int,int>
#define pll pair<long long, long long>
#define vi vector<int>
#define vl vector<long long>
#define pb push_back
#define rep(i, b) for(int i = 0; i < (b); ++i)
#define rep2(i,a,b) for(int i = a; i <= (b); ++i)
#define rep3(i,a,b,c) for(int i = a; i <= (b); i+=c)
#define count_bits(x) __builtin_popcountll((x))
#define all(x) (x).begin(),(x).end()
#define siz(x) (int)(x).size()
#define forall(it,x) for(auto& it:(x))
using namespace __gnu_pbds;
using namespace std;
typedef tree<int, null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> ordered_set;
mt19937 mt;void random_start(){mt.seed(chrono::time_point_cast<chrono::milliseconds>(chrono::high_resolution_clock::now()).time_since_epoch().count());}
ll los(ll a, ll b) {return a + (mt() % (b-a+1));}
const int INF = 1e9+50;
const ll INF_L = 1e18+40;
const ll MOD = 1e9+7;
struct frac
{
ll a;
ll b;
frac operator+(const frac& other)const
{
ll a2 = a*other.b + other.a*b;
ll b2 = b*other.b;
ll g = __gcd(a2,b2);
return {a2/g,b2/g};
}
frac operator-(const frac& other) const
{
ll a2 = a*other.b - other.a*b;
ll b2 = b*other.b;
ll g = __gcd(a2,b2);
return {a2/g,b2/g};
}
frac operator*(const frac& other) const
{
ll a2 = a*other.a;
ll b2 = b*other.b;
ll g = __gcd(a2,b2);
return {a2/g,b2/g};
}
frac operator/(const frac& other) const
{
ll a2 = a*other.b;
ll b2 = b*other.a;
ll g = __gcd(a2,b2);
return {a2/g,b2/g};
}
bool operator<(const frac& other) const
{
return a*other.b < other.a*b;
}
bool operator<=(const frac& other)
{
return a*other.b <= other.a*b;
}
bool operator>(const frac& other)
{
return a*other.b > other.a*b;
}
bool operator>=(const frac& other)
{
return a*other.b >= other.a*b;
}
};
ll L;
int n,m;
ll T[1001];
ll W[1001];
ll S[1001];
ll arr_time[1001][1001];
set<pll> end_sets[1001];
ll X;
void init(int L2, int N2, vl T2, vi W2, int X2, int M2, vi S2)
{
L = L2;
n = N2;
rep(i,n) T[i] = T2[i];
rep(i,n) W[i] = W2[i];
X = X2;
m = M2;
rep(i,m) S[i] = S2[i];
vector<pll> bus;
rep(i,n) bus.pb({W[i],T[i]});
sort(all(bus));
reverse(all(bus));
n = 0;
forall(it,bus)
{
if(it.ff <= X) break;
W[n] = it.ff;
T[n] = it.ss;
n++;
}
rep(i,n)
{
ll time_ = T[i];
rep(j,m-1)
{
arr_time[i][j] = time_;
auto nxt = end_sets[j].lower_bound({time_,-1e18});
if(nxt == end_sets[j].begin())
{
time_ += W[i] * (S[j+1] - S[j]);
continue;
}
nxt--;
if((*nxt).ss >= time_ + W[i]*(S[j+1]-S[j]))
{
time_ = (*nxt).ss;
}
else
{
time_ += W[i] * (S[j+1] - S[j]);
}
}
arr_time[i][m-1] = time_;
rep(j,m-1)
{
auto nxt = end_sets[j].lower_bound({arr_time[i][j]+1,-1e18});
if(nxt == end_sets[j].begin())
{
end_sets[j].insert({arr_time[i][j],arr_time[i][j+1]});
continue;
}
nxt--;
if((*nxt).ss >= arr_time[i][j+1]) continue;
while(true)
{
auto it = end_sets[j].lower_bound({arr_time[i][j],-1e18});
if(it == end_sets[j].begin()) break;
it--;
if((*it).ss <= arr_time[i][j+1])
{
end_sets[j].erase(it);
}
else break;
}
end_sets[j].insert({arr_time[i][j],arr_time[i][j+1]});
}
}
return;
}
ll arrival_time(ll time_)
{
int cur_stop = 0;
while(cur_stop != m-1)
{
pair<frac,int> com = {{(ll)1e18,1},-1};
rep(i,n)
{
frac oneX = {time_,X};
frac oneW = {arr_time[i][cur_stop],W[i]};
frac s1 = {S[cur_stop],1};
frac c = ((s1-oneW)-(s1-oneX)) * ((frac){X * W[i],1}) / (frac){W[i]-X,1};
//cerr << i << " " << c.a << "/" << c.b << " " << arr_time[i][cur_stop] << " " << W[i] << " xd\n";
if(c > (frac){time_,1})
{
com = min(com,{c,i});
}
}
// cerr <<cur_stop << " " << time_ << " " << com.ff.a << "/" << com.ff.b << " " << com.ss << " com\n";
if(com.ss == -1)
{
time_ += (S[m-1] - S[cur_stop]) * X;
return time_;
}
frac poz = (com.ff - (frac){time_,1}) * (frac){1,X} + (frac){S[cur_stop],1};
// cerr << poz.a << " " << poz.b << " poz\n";
int l = cur_stop;
int r = m-1;
int ans = -1;
while(l <= r)
{
int mid = (l+r)/2;
// cerr << mid << " " << S[mid] << " bin\n";
if((frac){S[mid],1} < poz)
{
ans = mid;
l = mid+1;
}
else
{
r = mid-1;
}
}
// cerr << ans << " ans\n";
if(ans == m-1)
{
time_ += (S[m-1] - S[cur_stop]) * X;
return time_;
}
time_ = arr_time[com.ss][ans+1];
cur_stop = ans+1;
}
return time_;
}
