#include "overtaking.h"
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <climits>
#include <cmath>
#include <complex>
#include <cstring>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <vector>
using namespace std;
using ll = long long;
using db = long double; // or double, if TL is tight
using str = string; // yay python!
// pairs
using pi = pair<int, int>;
using pl = pair<ll, ll>;
using pd = pair<db, db>;
#define mp make_pair
#define f first
#define s second
#define tcT template <class T
#define tcTU tcT, class U
// ^ lol this makes everything look weird but I'll try it
tcT > using V = vector<T>;
tcT, size_t SZ > using AR = array<T, SZ>;
using vi = V<int>;
using vb = V<bool>;
using vl = V<ll>;
using vd = V<db>;
using vs = V<str>;
using vpi = V<pi>;
using vpl = V<pl>;
using vpd = V<pd>;
// vectors
// oops size(x), rbegin(x), rend(x) need C++17
#define sz(x) int((x).size())
#define bg(x) begin(x)
#define all(x) bg(x), end(x)
#define rall(x) x.rbegin(), x.rend()
#define sor(x) sort(all(x))
#define rsz resize
#define ins insert
#define pb push_back
#define eb emplace_back
#define ft front()
#define bk back()
#define lb lower_bound
#define ub upper_bound
tcT > int lwb(V<T> &a, const T &b) { return int(lb(all(a), b) - bg(a)); }
tcT > int upb(V<T> &a, const T &b) { return int(ub(all(a), b) - bg(a)); }
// loops
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define F0R(i, a) FOR(i, 0, a)
#define ROF(i, a, b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i, a) ROF(i, 0, a)
#define rep(a) F0R(_, a)
#define each(a, x) for (auto &a : x)
const int MOD = (int)1e9 + 7; // 998244353;
const int MX = (int)2e5 + 5;
const ll BIG = 1e18; // not too close to LLONG_MAX
const db PI = acos((db)-1);
const int dx[4]{1, 0, -1, 0}, dy[4]{0, 1, 0, -1}; // for every grid problem!!
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>;
// bitwise ops
// also see https://gcc.gnu.org/onlinedocs/gcc/Other-Builtins.html
constexpr int pct(int x) { return __builtin_popcount(x); } // # of bits set
constexpr int bits(int x) { // assert(x >= 0); // make C++11 compatible until
// USACO updates ...
return x == 0 ? 0 : 31 - __builtin_clz(x);
} // floor(log2(x))
constexpr int p2(int x) { return 1 << x; }
constexpr int msk2(int x) { return p2(x) - 1; }
ll cdiv(ll a, ll b) {
return a / b + ((a ^ b) > 0 && a % b);
} // divide a by b rounded up
ll fdiv(ll a, ll b) {
return a / b - ((a ^ b) < 0 && a % b);
} // divide a by b rounded down
tcT > bool ckmin(T &a, const T &b) {
return b < a ? a = b, 1 : 0;
} // set a = min(a,b)
tcT > bool ckmax(T &a, const T &b) {
return a < b ? a = b, 1 : 0;
} // set a = max(a,b)
tcTU > T fstTrue(T lo, T hi, U f) {
++hi;
assert(lo <= hi); // assuming f is increasing
while (lo < hi) { // find first index such that f is true
T mid = lo + (hi - lo) / 2;
f(mid) ? hi = mid : lo = mid + 1;
}
return lo;
}
tcTU > T lstTrue(T lo, T hi, U f) {
--lo;
assert(lo <= hi); // assuming f is decreasing
while (lo < hi) { // find first index such that f is true
T mid = lo + (hi - lo + 1) / 2;
f(mid) ? lo = mid : hi = mid - 1;
}
return lo;
}
tcT > void remDup(vector<T> &v) { // sort and remove duplicates
sort(all(v));
v.erase(unique(all(v)), end(v));
}
tcTU > void safeErase(T &t, const U &u) {
auto it = t.find(u);
assert(it != end(t));
t.erase(it);
}
inline namespace IO {
#define SFINAE(x, ...) \
template <class, class = void> struct x : std::false_type {}; \
template <class T> struct x<T, std::void_t<__VA_ARGS__>> : std::true_type {}
SFINAE(DefaultI, decltype(std::cin >> std::declval<T &>()));
SFINAE(DefaultO, decltype(std::cout << std::declval<T &>()));
SFINAE(IsTuple, typename std::tuple_size<T>::type);
SFINAE(Iterable, decltype(std::begin(std::declval<T>())));
template <class T> constexpr char Space(const T &) {
return (Iterable<T>::value or IsTuple<T>::value) ? '\n' : ' ';
}
template <auto &is> struct Reader {
template <class T> void Impl(T &t) {
if constexpr (DefaultI<T>::value) is >> t;
else if constexpr (Iterable<T>::value) {
for (auto &x : t) Impl(x);
} else if constexpr (IsTuple<T>::value) {
std::apply([this](auto &...args) { (Impl(args), ...); }, t);
} else static_assert(IsTuple<T>::value, "No matching type for read");
}
template <class... Ts> void read(Ts &...ts) { ((Impl(ts)), ...); }
};
template <class... Ts> void re(Ts &...ts) { Reader<cin>{}.read(ts...); }
#define def(t, args...) \
t args; \
re(args);
template <auto &os, bool debug> struct Writer {
string comma() const { return debug ? "," : ""; }
template <class T> void Impl(T const &t) const {
if constexpr (DefaultO<T>::value) os << t;
else if constexpr (Iterable<T>::value) {
if (debug) os << '{';
int i = 0;
for (auto &&x : t)
((i++) ? (os << comma() << Space(x), Impl(x)) : Impl(x));
if (debug) os << '}';
} else if constexpr (IsTuple<T>::value) {
if (debug) os << '(';
std::apply(
[this](auto const &...args) {
int i = 0;
(((i++) ? (os << comma() << " ", Impl(args)) : Impl(args)),
...);
},
t);
if (debug) os << ')';
} else static_assert(IsTuple<T>::value, "No matching type for print");
}
template <class T> void ImplWrapper(T const &t) const {
if (debug) os << "\033[0;31m";
Impl(t);
if (debug) os << "\033[0m";
}
template <class... Ts> void print(Ts const &...ts) const {
((Impl(ts)), ...);
}
template <class F, class... Ts>
void print_with_sep(const std::string &sep, F const &f,
Ts const &...ts) const {
ImplWrapper(f), ((os << sep, ImplWrapper(ts)), ...), os << '\n';
}
void print_with_sep(const std::string &) const { os << '\n'; }
};
template <class... Ts> void pr(Ts const &...ts) {
Writer<cout, false>{}.print(ts...);
}
template <class... Ts> void ps(Ts const &...ts) {
Writer<cout, false>{}.print_with_sep(" ", ts...);
}
} // namespace IO
inline namespace Debug {
template <typename... Args> void err(Args... args) {
Writer<cerr, true>{}.print_with_sep(" | ", args...);
}
void err_prefix(str func, int line, string args) {
cerr << "\033[0;31m\u001b[1mDEBUG\033[0m"
<< " | "
<< "\u001b[34m" << func << "\033[0m"
<< ":"
<< "\u001b[34m" << line << "\033[0m"
<< " - "
<< "[" << args << "] = ";
}
#ifdef LOCAL
#define dbg(args...) err_prefix(__FUNCTION__, __LINE__, #args), err(args)
#else
#define dbg(...)
#endif
const auto beg_time = std::chrono::high_resolution_clock::now();
// https://stackoverflow.com/questions/47980498/accurate-c-c-clock-on-a-multi-core-processor-with-auto-overclock?noredirect=1&lq=1
double time_elapsed() {
return chrono::duration<double>(std::chrono::high_resolution_clock::now() -
beg_time)
.count();
}
} // namespace Debug
inline namespace FileIO {
void setIn(str s) { freopen(s.c_str(), "r", stdin); }
void setOut(str s) { freopen(s.c_str(), "w", stdout); }
void setIO(str s = "") {
cin.tie(0)->sync_with_stdio(0); // unsync C / C++ I/O streams
cout << fixed << setprecision(12);
// cin.exceptions(cin.failbit);
// throws exception when do smth illegal
// ex. try to read letter into int
if (sz(s)) setIn(s + ".in"), setOut(s + ".out"); // for old USACO
}
} // namespace FileIO
// struct Bus {
// ll T;
// int W;
// // bool operator<(const Bus &o) const { return W < o.W; }
// };
// V<Bus> buses;
V<vl> arrival_times;
V<vi> by_arrival_times;
vi S, W;
int X;
pair<ll, int> get_pair(int i, int x) {
return mp(arrival_times.at(i).at(x), W.at(x));
}
struct {
ll tot_shift_left = 0;
map<ll, ll> m;
void shift_left(ll c) { // f(x) -> y
// f_new(x-c) = y
tot_shift_left += c;
}
ll query(ll x) {
x += tot_shift_left;
auto it = m.ub(x);
if (it != begin(m)) ckmax(x, prev(it)->s);
return x;
}
void limit(ll x, ll y) {
x += tot_shift_left;
auto it = m.ub(x);
if (it != begin(m) && prev(it)->s >= y) return;
m[x] = y;
it = m.find(x);
while (next(it) != end(m) && next(it)->s <= y) m.erase(next(it));
}
} Container;
void init(int L, int N, std::vector<long long> T, std::vector<int> _W, int _X,
int M, std::vector<int> _S) {
W = _W;
X = _X;
S = _S;
assert(sz(S) == M);
// F0R(i, N) buses.pb(Bus{T[i], W[i]});
arrival_times.rsz(M);
arrival_times[0] = T;
// dbg("BEGIN INIT");
FOR(i, 1, M) {
arrival_times[i] = arrival_times[i - 1];
F0R(j, N) {
arrival_times[i][j] += (ll)W.at(j) * (S.at(i) - S.at(i - 1));
}
vi by_arrival_time(N);
iota(all(by_arrival_time), 0);
sort(all(by_arrival_time), [&](int x, int y) {
return get_pair(i - 1, x) < get_pair(i - 1, y);
});
by_arrival_times.pb(by_arrival_time);
ll max_arrival_time = 0;
for (int j : by_arrival_time) {
ckmax(max_arrival_time, arrival_times[i][j]);
ckmax(arrival_times[i][j], max_arrival_time);
}
}
// F0R(i, M) dbg(i, arrival_times[i]);
// dbg("DONE INIT");
R0F(i, M - 1) {
vpl pairs;
F0R(x, N) {
pairs.pb({arrival_times[i][x],
Container.query(arrival_times[i + 1][x])});
}
Container.shift_left((ll)X * (S[i + 1] - S[i]));
for (auto [p0, p1] : pairs) Container.limit(p0 + 1, p1);
}
}
long long arrival_time(long long Y) {
return Container.query(Y);
// F0R(i, sz(S) - 1) { // S[i] -> S[i+1]
// int j = lstTrue(0, sz(by_arrival_times[i]) - 1, [&](int idx) {
// return get_pair(i, by_arrival_times[i][idx]) < mp(Y, X);
// });
// // if (j != -1) {
// // dbg(i, j, by_arrival_times[i][j],
// // get_pair(i, by_arrival_times[i][j]));
// // }
// // dbg(i, j);
// Y += (ll)X * (S.at(i + 1) - S.at(i));
// if (j >= 0)
// ckmax(Y, arrival_times.at(i + 1).at(by_arrival_times.at(i).at(j)));
// // dbg(Y);
// }
// return Y;
}
