#include "overtaking.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef __int128 lll;
typedef long double ld;
typedef pair<ll, ll> pll;
typedef pair<ld, ld> pld;
#define MAX 9223372036854775807LL
#define MIN -9223372036854775807LL
#define INF 0x3f3f3f3f3f3f3f3f
#define fi first
#define se second
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); cout << fixed; cout.precision(10);
#define sp << " "
#define en << "\n"
#define compress(v) sort(v.begin(), v.end()), v.erase(unique(v.begin(), v.end()), v.end())
ll n, m, x;
ll LL;
ll w[2010];
ll S[2010][2010];
ll spd[2010];
ll siz;
vector<pll> qry;
vector<ll> zip;
ll won[8000010];
struct lazysegtree
{
ll lazy[8000010];
ll seg[8000010];
void prop(ll no, ll s, ll e)
{
if(!lazy[no])
return;
seg[no] = max(seg[no], lazy[no]);
if(s != e)
{
lazy[no << 1] = max(lazy[no << 1], lazy[no]);
lazy[no << 1 | 1] = max(lazy[no << 1 | 1], lazy[no]);
}
lazy[no] = 0;
}
void update(ll no, ll s, ll e, ll l, ll r, ll v)
{
prop(no, s, e);
if(e < l || r < s)
return;
if(l <= s && e <= r)
{
seg[no] = max(seg[no], v);
if(s != e)
{
lazy[no << 1] = max(lazy[no << 1], v);
lazy[no << 1 | 1] = max(lazy[no << 1 | 1], v);
}
return;
}
update(no << 1, s, (s + e) >> 1, l, r, v);
update(no << 1 | 1, ((s + e) >> 1) + 1, e, l, r, v);
seg[no] = max(seg[no << 1], seg[no << 1 | 1]);
}
ll query(ll no, ll s, ll e, ll l, ll r)
{
prop(no, s, e);
if(e < l || r < s)
return -INF;
if(l <= s && e <= r)
return seg[no];
return max(query(no << 1, s, (s + e) >> 1, l, r), query(no << 1 | 1, ((s + e) >> 1) + 1, e, l, r));
}
}segt;
ll num(ll X)
{
return lower_bound(zip.begin(), zip.end(), X) - zip.begin() + 1;
}
void init(int L, int N, vector<ll> T, vector<int> W, int X, int M, vector<int> SS)
{
x = X, LL = L;
for(ll i = 0 ; i < N ; i++)
{
if(W[i] <= X)
continue;
spd[++n] = W[i] - X;
S[1][n] = T[i];
}
for(ll i = 0 ; i < M ; i++)
w[++m] = SS[i];
for(ll i = 1 ; i < m ; i++)
{
vector< pair<pll, ll> > vv;
for(ll j = 1 ; j <= n ; j++)
vv.push_back({{S[i][j], spd[j]}, j});
sort(vv.begin(), vv.end());
ll maxx = 0;
ll dist = w[i + 1] - w[i];
for(auto &j : vv)
{
S[i + 1][j.se] = max(S[i][j.se] + dist * spd[j.se], maxx);
maxx = max(maxx, S[i + 1][j.se]);
}
}
for(ll i = 1 ; i < m ; i++)
{
vector<pll> vv;
for(ll j = 1 ; j <= n ; j++)
vv.push_back({S[i][j], S[i + 1][j]});
sort(vv.begin(), vv.end());
reverse(vv.begin(), vv.end());
for(ll j = 0 ; j < n ; j++)
qry.push_back(vv[j]);
}
for(auto &i : qry)
{
zip.push_back(i.fi + 1);
zip.push_back(i.se);
}
zip.push_back(0);
compress(zip);
siz = (ll)zip.size();
for(auto &i : zip)
segt.update(1, 1, siz, num(i), num(i), i);
for(ll i = (ll)qry.size() - 1 ; i >= 0 ; i--)
{
ll gap = segt.query(1, 1, siz, num(qry[i].se), num(qry[i].se));
segt.update(1, 1, siz, num(qry[i].fi + 1), num(qry[i].se), gap);
}
}
ll arrival_time(ll Y)
{
ll idx = upper_bound(zip.begin(), zip.end(), Y) - zip.begin();
ll gap = segt.query(1, 1, siz, idx, idx);
if(gap == zip[idx - 1])
return Y + x * LL;
return gap + x * LL;
}
