#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2")
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) (int)a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x,y) ((x+y-1)/(y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl
#define rep(i,n) for(int i = 0; i < n; ++i)
#define rep1(i,n) for(int i = 1; i <= n; ++i)
#define rev(i,s,e) for(int i = s; i >= e; --i)
#define trav(i,a) for(auto &i : a)
template<typename T>
void amin(T &a, T b) {
a = min(a,b);
}
template<typename T>
void amax(T &a, T b) {
a = max(a,b);
}
#ifdef LOCAL
#include "debug.h"
#else
#define debug(x) 42
#endif
/*
already knew some key ideas
*/
const int MOD = 1e9 + 7;
const int N = 1e3 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;
#include "overtaking.h"
template<typename T>
struct lazysegtree {
/*=======================================================*/
struct data {
ll a;
};
struct lazy {
ll a;
};
data d_neutral = {-1};
lazy l_neutral = {-1};
void merge(data &curr, data &left, data &right) {
curr.a = max(left.a,right.a);
}
void create(int x, int lx, int rx, T v) {
}
void modify(int x, int lx, int rx, T v) {
lz[x].a = v;
}
void propagate(int x, int lx, int rx) {
ll v = lz[x].a;
if(v == -1) return;
tr[x].a = v;
if(rx-lx > 1){
lz[x<<1].a = v;
lz[x<<1|1].a = v;
}
lz[x] = l_neutral;
}
/*=======================================================*/
int siz = 1;
vector<data> tr;
vector<lazy> lz;
lazysegtree() {
}
lazysegtree(int n) {
while (siz < n) siz *= 2;
tr.assign(2 * siz, d_neutral);
lz.assign(2 * siz, l_neutral);
}
void build(vector<T> &a, int n, int x, int lx, int rx) {
if (rx - lx == 1) {
if (lx < n) {
create(x, lx, rx, a[lx]);
}
return;
}
int mid = (lx + rx) >> 1;
build(a, n, x<<1, lx, mid);
build(a, n, x<<1|1, mid, rx);
merge(tr[x], tr[x<<1], tr[x<<1|1]);
}
void build(vector<T> &a, int n) {
build(a, n, 1, 0, siz);
}
void rupd(int l, int r, T v, int x, int lx, int rx) {
propagate(x, lx, rx);
if (lx >= r or rx <= l) return;
if (lx >= l and rx <= r) {
modify(x, lx, rx, v);
propagate(x, lx, rx);
return;
}
int mid = (lx + rx) >> 1;
rupd(l, r, v, x<<1, lx, mid);
rupd(l, r, v, x<<1|1, mid, rx);
merge(tr[x], tr[x<<1], tr[x<<1|1]);
}
void rupd(int l, int r, T v) {
rupd(l, r + 1, v, 1, 0, siz);
}
data query(int l, int r, int x, int lx, int rx) {
propagate(x, lx, rx);
if (lx >= r or rx <= l) return d_neutral;
if (lx >= l and rx <= r) return tr[x];
int mid = (lx + rx) >> 1;
data curr;
data left = query(l, r, x<<1, lx, mid);
data right = query(l, r, x<<1|1, mid, rx);
merge(curr, left, right);
return curr;
}
data query(int l, int r) {
return query(l, r + 1, 1, 0, siz);
}
};
vector<ll> T;
vector<int> W,S;
ll X,m;
vector<pll> segs;
lazysegtree<ll> st;
void init(int L, int n, std::vector<long long> T_, std::vector<int> W_, int X_, int M, std::vector<int> S_)
{
T = T_, W = W_, S = S_;
X = X_, m = M;
ll e[n][m], t[n][m];
rep(i,n){
e[i][0] = t[i][0] = T[i];
}
rep1(j,m-1){
rep(i,n){
e[i][j] = t[i][j-1]+(ll)W[i]*(S[j]-S[j-1]);
t[i][j] = e[i][j];
}
vector<pll> ord;
rep(i,n){
ord.pb({t[i][j-1],i});
}
sort(all(ord));
ll ptr = 0, mx = 0;
rep(i,n){
while(ptr < n and ord[ptr].ff < ord[i].ff){
amax(mx,e[ord[ptr].ss][j]);
ptr++;
}
amax(t[ord[i].ss][j],mx);
}
}
vector<ll> b;
rep(i,n){
rep(j,m){
b.pb(t[i][j]-X*S[j]);
}
}
sort(all(b));
b.resize(unique(all(b))-b.begin());
segs.pb({-inf2,b[0]-1});
rep(i,sz(b)){
segs.pb({b[i],b[i]});
if(i+1 < sz(b)){
segs.pb({b[i]+1,b[i+1]-1});
}
}
segs.pb({b.back()+1,inf2});
ll siz = sz(segs);
st = lazysegtree<ll>(siz);
ll f[n][m];
rep(i,n) f[i][m-1] = t[i][m-1];
rev(j,m-2,0){
vector<pll> ord;
rep(i,n){
ord.pb({t[i][j+1],i});
}
sort(all(ord));
for(auto [tv,i] : ord){
ll l = t[i][j]-X*S[j];
ll r = t[i][j+1]-X*S[j+1];
l = lower_bound(all(segs),pll{l,l})-segs.begin();
r = lower_bound(all(segs),pll{r,r})-segs.begin();
l++, r--;
st.rupd(l,r,f[i][j+1]);
}
rep(i,n){
ll val = t[i][j]-X*S[j];
ll ind = lower_bound(all(segs),pll{val,val})-segs.begin();
f[i][j] = max(t[i][j]+X*(S[m-1]-S[j]),st.query(ind,ind).a);
}
}
}
long long arrival_time(long long t)
{
ll ind = lower_bound(all(segs),pll{t+1,-1})-segs.begin()-1;
ll ans = max(t+X*S[m-1],st.query(ind,ind).a);
return ans;
}
