#include "overtaking.h"
#include <bits/stdc++.h>
//#include "debug.h"
using namespace std;
using ll = long long;
constexpr int MAX_SS = 1011;
// Lazy Segment Tree, copied from AtCoder {{{
// Source: https://github.com/atcoder/ac-library/blob/master/atcoder/lazysegtree.hpp
// Doc: https://atcoder.github.io/ac-library/master/document_en/lazysegtree.html
//
// Notes:
// - Index of elements from 0
// - Range queries are [l, r-1]
// - composition(f, g) should return f(g())
//
// Tested:
// - https://oj.vnoi.info/problem/qmax2
// - https://oj.vnoi.info/problem/lites
// - (range set, add, mult, sum) https://oj.vnoi.info/problem/segtree_itmix
// - (range add (i-L)*A + B, sum) https://oj.vnoi.info/problem/segtree_itladder
// - https://atcoder.jp/contests/practice2/tasks/practice2_l
// - https://judge.yosupo.jp/problem/range_affine_range_sum
int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (unsigned int)(n)) x++;
return x;
}
template<
class S, // node data type
S (*op) (S, S), // combine 2 nodes
S (*e) (), // identity element
class F, // lazy propagation tag
S (*mapping) (F, S), // apply tag F on a node
F (*composition) (F, F), // combine 2 tags
F (*id)() // identity tag
>
struct LazySegTree {
LazySegTree() : LazySegTree(0) {}
explicit LazySegTree(int n) : LazySegTree(vector<S>(n, e())) {}
explicit LazySegTree(const vector<S>& v) : _n((int) v.size()) {
log = ceil_pow2(_n);
size = 1 << log;
d = std::vector<S>(2 * size, e());
lz = std::vector<F>(size, id());
for (int i = 0; i < _n; i++) d[size + i] = v[i];
for (int i = size - 1; i >= 1; i--) {
update(i);
}
}
// 0 <= p < n
void set(int p, S x) {
assert(0 <= p && p < _n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
d[p] = x;
for (int i = 1; i <= log; i++) update(p >> i);
}
// 0 <= p < n
S get(int p) {
assert(0 <= p && p < _n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
return d[p];
}
// Get product in range [l, r-1]
// 0 <= l <= r <= n
// For empty segment (l == r) -> return e()
S prod(int l, int r) {
assert(0 <= l && l <= r && r <= _n);
if (l == r) return e();
l += size;
r += size;
for (int i = log; i >= 1; i--) {
if (((l >> i) << i) != l) push(l >> i);
if (((r >> i) << i) != r) push((r - 1) >> i);
}
S sml = e(), smr = e();
while (l < r) {
if (l & 1) sml = op(sml, d[l++]);
if (r & 1) smr = op(d[--r], smr);
l >>= 1;
r >>= 1;
}
return op(sml, smr);
}
S all_prod() {
return d[1];
}
// 0 <= p < n
void apply(int p, F f) {
assert(0 <= p && p < _n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
d[p] = mapping(f, d[p]);
for (int i = 1; i <= log; i++) update(p >> i);
}
// Apply f on all elements in range [l, r-1]
// 0 <= l <= r <= n
void apply(int l, int r, F f) {
assert(0 <= l && l <= r && r <= _n);
if (l == r) return;
l += size;
r += size;
for (int i = log; i >= 1; i--) {
if (((l >> i) << i) != l) push(l >> i);
if (((r >> i) << i) != r) push((r - 1) >> i);
}
{
int l2 = l, r2 = r;
while (l < r) {
if (l & 1) all_apply(l++, f);
if (r & 1) all_apply(--r, f);
l >>= 1;
r >>= 1;
}
l = l2;
r = r2;
}
for (int i = 1; i <= log; i++) {
if (((l >> i) << i) != l) update(l >> i);
if (((r >> i) << i) != r) update((r - 1) >> i);
}
}
// Binary search on SegTree to find largest r:
// f(op(a[l] .. a[r-1])) = true (assuming empty array is always true)
// f(op(a[l] .. a[r])) = false (assuming op(..., a[n]), which is out of bound, is always false)
template <bool (*g)(S)> int max_right(int l) {
return max_right(l, [](S x) { return g(x); });
}
template <class G> int max_right(int l, G g) {
assert(0 <= l && l <= _n);
assert(g(e()));
if (l == _n) return _n;
l += size;
for (int i = log; i >= 1; i--) push(l >> i);
S sm = e();
do {
while (l % 2 == 0) l >>= 1;
if (!g(op(sm, d[l]))) {
while (l < size) {
push(l);
l = (2 * l);
if (g(op(sm, d[l]))) {
sm = op(sm, d[l]);
l++;
}
}
return l - size;
}
sm = op(sm, d[l]);
l++;
} while ((l & -l) != l);
return _n;
}
// Binary search on SegTree to find smallest l:
// f(op(a[l] .. a[r-1])) = true (assuming empty array is always true)
// f(op(a[l-1] .. a[r-1])) = false (assuming op(a[-1], ..), which is out of bound, is always false)
template <bool (*g)(S)> int min_left(int r) {
return min_left(r, [](S x) { return g(x); });
}
template <class G> int min_left(int r, G g) {
assert(0 <= r && r <= _n);
assert(g(e()));
if (r == 0) return 0;
r += size;
for (int i = log; i >= 1; i--) push((r - 1) >> i);
S sm = e();
do {
r--;
while (r > 1 && (r % 2)) r >>= 1;
if (!g(op(d[r], sm))) {
while (r < size) {
push(r);
r = (2 * r + 1);
if (g(op(d[r], sm))) {
sm = op(d[r], sm);
r--;
}
}
return r + 1 - size;
}
sm = op(d[r], sm);
} while ((r & -r) != r);
return 0;
}
private:
int _n, size, log;
vector<S> d;
vector<F> lz;
void update(int k) {
d[k] = op(d[2*k], d[2*k+1]);
}
void all_apply(int k, F f) {
d[k] = mapping(f, d[k]);
if (k < size) lz[k] = composition(f, lz[k]);
}
void push(int k) {
all_apply(2*k, lz[k]);
all_apply(2*k+1, lz[k]);
lz[k] = id();
}
};
// }}}
ll op(ll x, ll y) { return max(x, y); }
ll e() { return 0ll; }
ll mapping(ll f, ll s) { return max(s, f); }
ll composition(ll f, ll g) { return max(f, g); }
ll id() { return 0ll; }
// lines[i]: stores lines between i-th and (i+1)-th sorting stations
// each line is represented by its 2 endpoints
set<pair<ll, ll>> lines[MAX_SS];
int M;
ll X;
vector<int> S;
vector<ll> xs;
using STMax = LazySegTree<ll, op, e, ll, mapping, composition, id>;
STMax st;
void init(
int L,
int nBus, vector<ll> T, vector<int> W,
int _X,
int _M, vector<int> _S) {
// subtask 4 {{{
M = _M;
X = _X;
S = _S;
// sort buses in decreasing order of W (so slowest buses are processed first)
vector<pair<ll, ll>> buses;
for (int i = 0; i < nBus; ++i) {
if (W[i] <= X) continue;
buses.emplace_back(W[i], T[i]);
}
std::sort(buses.begin(), buses.end());
std::reverse(buses.begin(), buses.end());
// init gaps between 2 sorting stations
for (int i = 0; i < M-1; ++i) { // only M-1 gaps
lines[i].clear();
lines[i].insert({0, 0});
}
// for each bus, add its line to all gaps
for (const auto& [w, t] : buses) {
ll cur_time = t;
for (int j = 0; j < M-1; ++j) {
auto it = std::prev(lines[j].lower_bound({cur_time, 0}));
ll exit_time = std::max(it->second, cur_time + w*(S[j+1] - S[j]));
lines[j].insert({cur_time, exit_time});
cur_time = exit_time;
}
}
// }}}
for (int i = M-2; i >= 0; --i) {
for (auto [l, r] : lines[i]) {
if (!l && !r) continue;
xs.push_back(l - X*S[i] + 1);
xs.push_back(r - X*S[i+1]);
}
}
std::sort(xs.begin(), xs.end());
xs.erase(unique(xs.begin(), xs.end()), xs.end());
st = STMax(xs);
for (int i = M-2; i >= 0; --i) {
for (auto [l, r] : lines[i]) {
if (!l && !r) continue;
int u = lower_bound(xs.begin(), xs.end(), l - X*S[i] + 1) - xs.begin();
int v = lower_bound(xs.begin(), xs.end(), r - X*S[i+1]) - xs.begin();
st.apply(u, v+1, st.get(v));
}
}
}
ll arrival_time(ll Y) {
ll tx = X * (ll) S.back();
if (xs.empty() || Y < xs[0] || Y > xs.back()) return tx + Y;
return tx + max(Y, st.get(upper_bound(xs.begin(), xs.end(), Y) - xs.begin() - 1));
}
