/*************************************
* author: marvinthang *
* created: 19.01.2024 10:11:16 *
*************************************/
#include "overtaking.h"
#include <bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define left ___left
#define right ___right
#define TIME (1.0 * clock() / CLOCKS_PER_SEC)
#define MASK(i) (1LL << (i))
#define BIT(x, i) ((x) >> (i) & 1)
#define __builtin_popcount __builtin_popcountll
#define ALL(v) (v).begin(), (v).end()
#define REP(i, n) for (int i = 0, _n = (n); i < _n; ++i)
#define REPD(i, n) for (int i = (n); i-- > 0; )
#define FOR(i, a, b) for (int i = (a), _b = (b); i < _b; ++i)
#define FORD(i, b, a) for (int i = (b), _a = (a); --i >= _a; )
#define FORE(i, a, b) for (int i = (a), _b = (b); i <= _b; ++i)
#define FORDE(i, b, a) for (int i = (b), _a = (a); i >= _a; --i)
#define scan_op(...) istream & operator >> (istream &in, __VA_ARGS__ &u)
#define print_op(...) ostream & operator << (ostream &out, const __VA_ARGS__ &u)
#ifdef LOCAL
#include "debug.h"
#else
#define file(name) if (fopen(name".inp", "r")) { freopen(name".inp", "r", stdin); freopen(name".out", "w", stdout); }
#define DB(...) 23
#define db(...) 23
#define debug(...) 23
#endif
template <class U, class V> scan_op(pair <U, V>) { return in >> u.first >> u.second; }
template <class T> scan_op(vector <T>) { for (size_t i = 0; i < u.size(); ++i) in >> u[i]; return in; }
template <class U, class V> print_op(pair <U, V>) { return out << '(' << u.first << ", " << u.second << ')'; }
template <size_t i, class T> ostream & print_tuple_utils(ostream &out, const T &tup) { if constexpr(i == tuple_size<T>::value) return out << ")"; else return print_tuple_utils<i + 1, T>(out << (i ? ", " : "(") << get<i>(tup), tup); }
template <class ...U> print_op(tuple<U...>) { return print_tuple_utils<0, tuple<U...>>(out, u); }
template <class Con, class = decltype(begin(declval<Con>()))> typename enable_if <!is_same<Con, string>::value, ostream&>::type operator << (ostream &out, const Con &con) { out << '{'; for (__typeof(con.begin()) it = con.begin(); it != con.end(); ++it) out << (it == con.begin() ? "" : ", ") << *it; return out << '}'; }
template <class A, class B> bool minimize(A &a, B b) { return a > b ? a = b, true : false; }
template <class A, class B> bool maximize(A &a, B b) { return a < b ? a = b, true : false; }
// end of template
int n;
vector <long long> cx, st;
long long add;
void init(int L, int N, vector <long long> T, vector <int> W, int X, int M, vector <int> S) {
add = 1LL * X * L;
vector <pair <long long, int>> buses;
REP(i, N) buses.emplace_back(T[i], W[i]);
vector <vector <pair <long long, long long>>> lines(M - 1);
REP(t, M - 1) {
sort(ALL(buses));
int dist = S[t + 1] - S[t];
REP(i, N) {
long long nxt = buses[i].fi + 1LL * buses[i].se * dist;
if (i && nxt <= buses[i - 1].fi) nxt = buses[i - 1].fi;
else {
long long tl = buses[i].fi - 1LL * X * S[t] + 1;
long long tr = nxt - 1LL * X * S[t + 1];
if (tl >= 0 && tl < tr) {
lines[t].emplace_back(tl, tr);
cx.push_back(tl);
cx.push_back(tr);
}
}
buses[i].fi = nxt;
}
}
sort(ALL(cx));
cx.erase(unique(ALL(cx)), cx.end());
n = cx.size();
st.resize(2 * n);
REP(i, n) st[i + n] = cx[i];
REPD(t, M - 1) {
for (auto &[l, r]: lines[t]) {
int tl = lower_bound(ALL(cx), l) - cx.begin();
int tr = lower_bound(ALL(cx), r) - cx.begin();
if (tl < tr) {
long long val = 0;
for (int i = tr + n; i; i >>= 1) maximize(val, st[i]);
for (tl += n, tr += n; tl < tr; tl >>= 1, tr >>= 1) {
if (tl & 1) maximize(st[tl++], val);
if (tr & 1) maximize(st[--tr], val);
}
}
}
}
FOR(i, 1, n) if (st[i]) {
maximize(st[i << 1], st[i]);
maximize(st[i << 1 | 1], st[i]);
}
}
long long arrival_time(long long Y) {
if (Y < cx[0]) return Y + add;
return add + max(Y, st[upper_bound(ALL(cx), Y) - cx.begin() - 1 + n]);
return 0;
}
