// #pragma GCC target("avx2") // #pragma GCC optimize("O3") // #pragma GCC optimize("unroll-loops") // #define INTERACTIVE #include using namespace std; namespace templates { // type using ll = long long; using ull = unsigned long long; using Pii = pair; using Pil = pair; using Pli = pair; using Pll = pair; template using pq = priority_queue; template using qp = priority_queue, greater>; // clang-format off #define vec(T, A, ...) vector A(__VA_ARGS__); #define vvec(T, A, h, ...) vector> A(h, vector(__VA_ARGS__)); #define vvvec(T, A, h1, h2, ...) vector>> A(h1, vector>(h2, vector(__VA_ARGS__))); // clang-format on // for loop #define fori1(a) for (ll _ = 0; _ < (a); _++) #define fori2(i, a) for (ll i = 0; i < (a); i++) #define fori3(i, a, b) for (ll i = (a); i < (b); i++) #define fori4(i, a, b, c) for (ll i = (a); ((c) > 0 || i > (b)) && ((c) < 0 || i < (b)); i += (c)) #define overload4(a, b, c, d, e, ...) e #define fori(...) overload4(__VA_ARGS__, fori4, fori3, fori2, fori1)(__VA_ARGS__) // declare and input // clang-format off #define INT(...) int __VA_ARGS__; inp(__VA_ARGS__); #define LL(...) ll __VA_ARGS__; inp(__VA_ARGS__); #define STRING(...) string __VA_ARGS__; inp(__VA_ARGS__); #define CHAR(...) char __VA_ARGS__; inp(__VA_ARGS__); #define DOUBLE(...) double __VA_ARGS__; STRING(str___); __VA_ARGS__ = stod(str___); #define VEC(T, A, n) vector A(n); inp(A); #define VVEC(T, A, n, m) vector> A(n, vector(m)); inp(A); // clang-format on // const value const ll MOD1 = 1000000007; const ll MOD9 = 998244353; const double PI = acos(-1); // other macro #if !defined(RIN__LOCAL) && !defined(INTERACTIVE) #define endl "\n" #endif #define spa ' ' #define len(A) ll(A.size()) #define all(A) begin(A), end(A) // function vector stoc(string &S) { int n = S.size(); vector ret(n); for (int i = 0; i < n; i++) ret[i] = S[i]; return ret; } string ctos(vector &S) { int n = S.size(); string ret = ""; for (int i = 0; i < n; i++) ret += S[i]; return ret; } template auto min(const T &a) { return *min_element(all(a)); } template auto max(const T &a) { return *max_element(all(a)); } template auto clamp(T &a, const S &l, const S &r) { return (a > r ? r : a < l ? l : a); } template inline bool chmax(T &a, const S &b) { return (a < b ? a = b, 1 : 0); } template inline bool chmin(T &a, const S &b) { return (a > b ? a = b, 1 : 0); } template inline bool chclamp(T &a, const S &l, const S &r) { auto b = clamp(a, l, r); return (a != b ? a = b, 1 : 0); } template T sum(vector &A) { T tot = 0; for (auto a : A) tot += a; return tot; } template vector compression(vector X) { sort(all(X)); X.erase(unique(all(X)), X.end()); return X; } // input and output namespace io { // __int128_t std::ostream &operator<<(std::ostream &dest, __int128_t value) { std::ostream::sentry s(dest); if (s) { __uint128_t tmp = value < 0 ? -value : value; char buffer[128]; char *d = std::end(buffer); do { --d; *d = "0123456789"[tmp % 10]; tmp /= 10; } while (tmp != 0); if (value < 0) { --d; *d = '-'; } int len = std::end(buffer) - d; if (dest.rdbuf()->sputn(d, len) != len) { dest.setstate(std::ios_base::badbit); } } return dest; } // vector template istream &operator>>(istream &is, vector &A) { for (auto &a : A) is >> a; return is; } template ostream &operator<<(ostream &os, vector &A) { for (size_t i = 0; i < A.size(); i++) { os << A[i]; if (i != A.size() - 1) os << ' '; } return os; } // vector> template istream &operator>>(istream &is, vector> &A) { for (auto &a : A) is >> a; return is; } template ostream &operator<<(ostream &os, vector> &A) { for (size_t i = 0; i < A.size(); i++) { os << A[i]; if (i != A.size() - 1) os << endl; } return os; } // pair template istream &operator>>(istream &is, pair &A) { is >> A.first >> A.second; return is; } template ostream &operator<<(ostream &os, pair &A) { os << A.first << ' ' << A.second; return os; } // vector> template istream &operator>>(istream &is, vector> &A) { for (size_t i = 0; i < A.size(); i++) { is >> A[i]; } return is; } template ostream &operator<<(ostream &os, vector> &A) { for (size_t i = 0; i < A.size(); i++) { os << A[i]; if (i != A.size() - 1) os << endl; } return os; } // tuple template struct TuplePrint { static ostream &print(ostream &os, const T &t) { TuplePrint::print(os, t); os << ' ' << get(t); return os; } }; template struct TuplePrint { static ostream &print(ostream &os, const T &t) { os << get<0>(t); return os; } }; template ostream &operator<<(ostream &os, const tuple &t) { TuplePrint::print(os, t); return os; } // io functions void FLUSH() { cout << flush; } void print() { cout << endl; } template void print(Head &&head, Tail &&...tail) { cout << head; if (sizeof...(Tail)) cout << spa; print(std::forward(tail)...); } template void prisep(vector &A, S sep) { int n = A.size(); for (int i = 0; i < n; i++) { cout << A[i]; if (i != n - 1) cout << sep; } cout << endl; } template void priend(T A, S end) { cout << A << end; } template void prispa(T A) { priend(A, spa); } template bool printif(bool f, T A, S B) { if (f) print(A); else print(B); return f; } template void inp(T &...a) { (cin >> ... >> a); } } // namespace io using namespace io; // read graph vector> read_edges(int n, int m, bool direct = false, int indexed = 1) { vector> edges(n, vector()); for (int i = 0; i < m; i++) { INT(u, v); u -= indexed; v -= indexed; edges[u].push_back(v); if (!direct) edges[v].push_back(u); } return edges; } vector> read_tree(int n, int indexed = 1) { return read_edges(n, n - 1, false, indexed); } template vector>> read_wedges(int n, int m, bool direct = false, int indexed = 1) { vector>> edges(n, vector>()); for (int i = 0; i < m; i++) { INT(u, v); T w; inp(w); u -= indexed; v -= indexed; edges[u].push_back({v, w}); if (!direct) edges[v].push_back({u, w}); } return edges; } template vector>> read_wtree(int n, int indexed = 1) { return read_wedges(n, n - 1, false, indexed); } // yes / no namespace yesno { // yes inline bool yes(bool f = true) { cout << (f ? "yes" : "no") << endl; return f; } inline bool Yes(bool f = true) { cout << (f ? "Yes" : "No") << endl; return f; } inline bool YES(bool f = true) { cout << (f ? "YES" : "NO") << endl; return f; } // no inline bool no(bool f = true) { cout << (!f ? "yes" : "no") << endl; return f; } inline bool No(bool f = true) { cout << (!f ? "Yes" : "No") << endl; return f; } inline bool NO(bool f = true) { cout << (!f ? "YES" : "NO") << endl; return f; } // possible inline bool possible(bool f = true) { cout << (f ? "possible" : "impossible") << endl; return f; } inline bool Possible(bool f = true) { cout << (f ? "Possible" : "Impossible") << endl; return f; } inline bool POSSIBLE(bool f = true) { cout << (f ? "POSSIBLE" : "IMPOSSIBLE") << endl; return f; } // impossible inline bool impossible(bool f = true) { cout << (!f ? "possible" : "impossible") << endl; return f; } inline bool Impossible(bool f = true) { cout << (!f ? "Possible" : "Impossible") << endl; return f; } inline bool IMPOSSIBLE(bool f = true) { cout << (!f ? "POSSIBLE" : "IMPOSSIBLE") << endl; return f; } // Alice Bob inline bool Alice(bool f = true) { cout << (f ? "Alice" : "Bob") << endl; return f; } inline bool Bob(bool f = true) { cout << (f ? "Bob" : "Alice") << endl; return f; } // Takahashi Aoki inline bool Takahashi(bool f = true) { cout << (f ? "Takahashi" : "Aoki") << endl; return f; } inline bool Aoki(bool f = true) { cout << (f ? "Aoki" : "Takahashi") << endl; return f; } } // namespace yesno using namespace yesno; } // namespace templates using namespace templates; // #include "data_structure/segTree.hpp" /////// https://hitonanode.github.io/cplib-cpp/segmenttree/rangetree.hpp.html #ifndef ATCODER_SEGTREE_HPP #define ATCODER_SEGTREE_HPP 1 #include #include #include #ifndef ATCODER_INTERNAL_BITOP_HPP #define ATCODER_INTERNAL_BITOP_HPP 1 #ifdef _MSC_VER #include #endif namespace atcoder { namespace internal { // @param n `0 <= n` // @return minimum non-negative `x` s.t. `n <= 2**x` int ceil_pow2(int n) { int x = 0; while ((1U << x) < (unsigned int)(n)) x++; return x; } // @param n `1 <= n` // @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0` constexpr int bsf_constexpr(unsigned int n) { int x = 0; while (!(n & (1 << x))) x++; return x; } // @param n `1 <= n` // @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0` int bsf(unsigned int n) { #ifdef _MSC_VER unsigned long index; _BitScanForward(&index, n); return index; #else return __builtin_ctz(n); #endif } } // namespace internal } // namespace atcoder #endif // ATCODER_INTERNAL_BITOP_HPP namespace atcoder { template struct segtree { public: segtree() : segtree(0) {} explicit segtree(int n) : segtree(std::vector(n, e())) {} explicit segtree(const std::vector &v) : _n(int(v.size())) { log = internal::ceil_pow2(_n); size = 1 << log; d = std::vector(2 * size, e()); for (int i = 0; i < _n; i++) d[size + i] = v[i]; for (int i = size - 1; i >= 1; i--) { update(i); } } void set(int p, S x) { assert(0 <= p && p < _n); p += size; d[p] = x; for (int i = 1; i <= log; i++) update(p >> i); } S get(int p) const { assert(0 <= p && p < _n); return d[p + size]; } S prod(int l, int r) const { assert(0 <= l && l <= r && r <= _n); S sml = e(), smr = e(); l += size; r += size; 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() const { return d[1]; } template int max_right(int l) const { return max_right(l, [](S x) { return f(x); }); } template int max_right(int l, F f) const { assert(0 <= l && l <= _n); assert(f(e())); if (l == _n) return _n; l += size; S sm = e(); do { while (l % 2 == 0) l >>= 1; if (!f(op(sm, d[l]))) { while (l < size) { l = (2 * l); if (f(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; } template int min_left(int r) const { return min_left(r, [](S x) { return f(x); }); } template int min_left(int r, F f) const { assert(0 <= r && r <= _n); assert(f(e())); if (r == 0) return 0; r += size; S sm = e(); do { r--; while (r > 1 && (r % 2)) r >>= 1; if (!f(op(d[r], sm))) { while (r < size) { r = (2 * r + 1); if (f(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; std::vector d; void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); } }; } // namespace atcoder #endif // ATCODER_SEGTREE_HPP // CUT begin // 逆元を要求しない領域木 template class rangetree { int n; using Pt = std::pair; std::vector _pts; std::vector> _range2yxs; std::vector> segtrees; void _set(int v, Pt p, S val) { auto i = std::distance( _range2yxs[v].begin(), std::lower_bound(_range2yxs[v].begin(), _range2yxs[v].end(), Pt{p.second, p.first})); segtrees[v].set(i, val); } void _add(int v, Pt p, S val) { auto i = std::distance( _range2yxs[v].begin(), std::lower_bound(_range2yxs[v].begin(), _range2yxs[v].end(), Pt{p.second, p.first})); segtrees[v].set(i, op(segtrees[v].get(i), val)); } S _prod(int v, Coordinate yl, Coordinate yr) const { auto comp = [&](const Pt &l, const Pt &r) { return l.first < r.first; }; auto il = std::distance( _range2yxs[v].begin(), std::lower_bound(_range2yxs[v].begin(), _range2yxs[v].end(), Pt{yl, yl}, comp)); auto ir = std::distance( _range2yxs[v].begin(), std::lower_bound(_range2yxs[v].begin(), _range2yxs[v].end(), Pt{yr, yr}, comp)); return segtrees[v].prod(il, ir); } public: rangetree() = default; void add_point(Coordinate x, Coordinate y) noexcept { _pts.emplace_back(x, y); } void build() { std::sort(_pts.begin(), _pts.end()); _pts.erase(std::unique(_pts.begin(), _pts.end()), _pts.end()); n = _pts.size(); _range2yxs.resize(n * 2); for (int i = 0; i < n; i++) _range2yxs[n + i] = {{_pts[i].second, _pts[i].first}}; for (int i = n - 1; i > 0; i--) { auto &lch = _range2yxs[i * 2]; auto &rch = _range2yxs[i * 2 + 1]; std::merge(lch.begin(), lch.end(), rch.begin(), rch.end(), std::back_inserter(_range2yxs[i])); _range2yxs[i].erase(std::unique(_range2yxs[i].begin(), _range2yxs[i].end()), _range2yxs[i].end()); } for (const auto &v : _range2yxs) segtrees.emplace_back(v.size()); } void set(Coordinate x, Coordinate y, S val) { int i = std::distance(_pts.begin(), std::lower_bound(_pts.begin(), _pts.end(), Pt{x, y})); assert(i < n and _pts[i] == std::make_pair(x, y)); for (i += n; i; i >>= 1) _set(i, {x, y}, val); } void add(Coordinate x, Coordinate y, S val) { int i = std::distance(_pts.begin(), std::lower_bound(_pts.begin(), _pts.end(), Pt{x, y})); assert(i < n and _pts[i] == std::make_pair(x, y)); for (i += n; i; i >>= 1) _add(i, {x, y}, val); } S prod(Coordinate xl, Coordinate xr, Coordinate yl, Coordinate yr) const { auto comp = [](const Pt &l, const Pt &r) { return l.first < r.first; }; int l = n + std::distance(_pts.begin(), std::lower_bound(_pts.begin(), _pts.end(), Pt{xl, yr}, comp)); int r = n + std::distance(_pts.begin(), std::lower_bound(_pts.begin(), _pts.end(), Pt{xr, yr}, comp)); S ret = e(); while (l < r) { if (l & 1) ret = op(ret, _prod(l++, yl, yr)); if (r & 1) ret = op(ret, _prod(--r, yl, yr)); l >>= 1, r >>= 1; } return ret; } S get(Coordinate x, Coordinate y) const { return prod(x, x + 1, y, y + 1); } }; const ll inf = 1LL << 60; using S = ll; S op(S l, S r) { return l > r ? l : r; } S e() { return -inf; } void solve() { LL(n, K); VEC(ll, T, n); VEC(ll, X, n); VEC(ll, C, n); vec(int, ind, n); iota(all(ind), 0); sort(all(ind), [&](int i, int j) { return T[i] < T[j]; }); rangetree seg_R; rangetree seg_L; vec(ll, add, n); vec(ll, sub, n); add.push_back(0); sub.push_back(0); fori(i, n) { add[i] = X[i] + K * T[i]; sub[i] = X[i] - K * T[i]; } add = compression(add); sub = compression(sub); auto X2 = X; X2.push_back(0); X2 = compression(X2); fori(i, n) { int xp = lower_bound(all(X2), X[i]) - X2.begin(); int ap = lower_bound(all(add), X[i] + K * T[i]) - add.begin(); int sp = lower_bound(all(sub), X[i] - K * T[i]) - sub.begin(); seg_R.add_point(xp, ap); seg_L.add_point(xp, sp); } { int xp = lower_bound(all(X2), 0) - X2.begin(); int ap = lower_bound(all(add), 0) - add.begin(); int sp = lower_bound(all(sub), 0) - sub.begin(); seg_R.add_point(xp, ap); seg_L.add_point(xp, sp); seg_R.build(); seg_L.build(); seg_R.set(xp, ap, 0); seg_L.set(xp, sp, 0); } ll ans = 0; for (auto i : ind) { int xp = lower_bound(all(X2), X[i]) - X2.begin(); int ap = lower_bound(all(add), X[i] + K * T[i]) - add.begin(); int sp = lower_bound(all(sub), X[i] - K * T[i]) - sub.begin(); ll r = seg_R.prod(xp, len(X2), 0, ap); ll l = seg_L.prod(0, xp, sp, len(sub)); ll ma = max(r, l) + C[i]; chmax(ans, ma); seg_R.set(xp, ap, ma); seg_L.set(xp, sp, ma); } print(ans); } int main() { #ifndef INTERACTIVE std::cin.tie(0)->sync_with_stdio(0); #endif // std::cout << std::fixed << std::setprecision(12); int t; t = 1; // std::cin >> t; while (t--) solve(); return 0; } // // #pragma GCC target("avx2") // // #pragma GCC optimize("O3") // // #pragma GCC optimize("unroll-loops") // // #define INTERACTIVE // // #include "kyopro-cpp/template.hpp" // // // #include "data_structure/segTree.hpp" // // /////// https://hitonanode.github.io/cplib-cpp/segmenttree/rangetree.hpp.html // #include "atcoder/segtree.hpp" // // // CUT begin // // 逆元を要求しない領域木 // template // class rangetree { // int n; // using Pt = std::pair; // std::vector _pts; // std::vector> _range2yxs; // std::vector> segtrees; // void _set(int v, Pt p, S val) { // auto i = std::distance( // _range2yxs[v].begin(), // std::lower_bound(_range2yxs[v].begin(), _range2yxs[v].end(), Pt{p.second, p.first})); // segtrees[v].set(i, val); // } // void _add(int v, Pt p, S val) { // auto i = std::distance( // _range2yxs[v].begin(), // std::lower_bound(_range2yxs[v].begin(), _range2yxs[v].end(), Pt{p.second, p.first})); // segtrees[v].set(i, op(segtrees[v].get(i), val)); // } // S _prod(int v, Coordinate yl, Coordinate yr) const { // auto comp = [&](const Pt &l, const Pt &r) { return l.first < r.first; }; // auto il = std::distance( // _range2yxs[v].begin(), // std::lower_bound(_range2yxs[v].begin(), _range2yxs[v].end(), Pt{yl, yl}, comp)); // auto ir = std::distance( // _range2yxs[v].begin(), // std::lower_bound(_range2yxs[v].begin(), _range2yxs[v].end(), Pt{yr, yr}, comp)); // return segtrees[v].prod(il, ir); // } // // public: // rangetree() = default; // void add_point(Coordinate x, Coordinate y) noexcept { // _pts.emplace_back(x, y); // } // void build() { // std::sort(_pts.begin(), _pts.end()); // _pts.erase(std::unique(_pts.begin(), _pts.end()), _pts.end()); // n = _pts.size(); // // _range2yxs.resize(n * 2); // for (int i = 0; i < n; i++) _range2yxs[n + i] = {{_pts[i].second, _pts[i].first}}; // for (int i = n - 1; i > 0; i--) { // auto &lch = _range2yxs[i * 2]; // auto &rch = _range2yxs[i * 2 + 1]; // std::merge(lch.begin(), lch.end(), rch.begin(), rch.end(), // std::back_inserter(_range2yxs[i])); // _range2yxs[i].erase(std::unique(_range2yxs[i].begin(), _range2yxs[i].end()), // _range2yxs[i].end()); // } // for (const auto &v : _range2yxs) segtrees.emplace_back(v.size()); // } // void set(Coordinate x, Coordinate y, S val) { // int i = std::distance(_pts.begin(), std::lower_bound(_pts.begin(), _pts.end(), Pt{x, // y})); assert(i < n and _pts[i] == std::make_pair(x, y)); for (i += n; i; i >>= 1) _set(i, // {x, y}, val); // } // void add(Coordinate x, Coordinate y, S val) { // int i = std::distance(_pts.begin(), std::lower_bound(_pts.begin(), _pts.end(), Pt{x, // y})); assert(i < n and _pts[i] == std::make_pair(x, y)); for (i += n; i; i >>= 1) _add(i, // {x, y}, val); // } // S prod(Coordinate xl, Coordinate xr, Coordinate yl, Coordinate yr) const { // auto comp = [](const Pt &l, const Pt &r) { return l.first < r.first; }; // int l = n + std::distance(_pts.begin(), // std::lower_bound(_pts.begin(), _pts.end(), Pt{xl, yr}, // comp)); // int r = n + std::distance(_pts.begin(), // std::lower_bound(_pts.begin(), _pts.end(), Pt{xr, yr}, // comp)); // S ret = e(); // while (l < r) { // if (l & 1) ret = op(ret, _prod(l++, yl, yr)); // if (r & 1) ret = op(ret, _prod(--r, yl, yr)); // l >>= 1, r >>= 1; // } // return ret; // } // S get(Coordinate x, Coordinate y) const { // return prod(x, x + 1, y, y + 1); // } // }; // // const ll inf = 1LL << 60; // using S = ll; // S op(S l, S r) { // return l > r ? l : r; // } // S e() { // return -inf; // } // // void solve() { // LL(n, K); // VEC(ll, T, n); // VEC(ll, X, n); // VEC(ll, C, n); // vec(int, ind, n); // iota(all(ind), 0); // sort(all(ind), [&](int i, int j) { return T[i] < T[j]; }); // // rangetree seg_R; // rangetree seg_L; // vec(ll, add, n); // vec(ll, sub, n); // add.push_back(0); // sub.push_back(0); // fori(i, n) { // add[i] = X[i] + K * T[i]; // sub[i] = X[i] - K * T[i]; // } // add = compression(add); // sub = compression(sub); // auto X2 = X; // X2.push_back(0); // X2 = compression(X2); // // fori(i, n) { // int xp = lower_bound(all(X2), X[i]) - X2.begin(); // int ap = lower_bound(all(add), X[i] + K * T[i]) - add.begin(); // int sp = lower_bound(all(sub), X[i] - K * T[i]) - sub.begin(); // seg_R.add_point(xp, ap); // seg_L.add_point(xp, sp); // } // // { // int xp = lower_bound(all(X2), 0) - X2.begin(); // int ap = lower_bound(all(add), 0) - add.begin(); // int sp = lower_bound(all(sub), 0) - sub.begin(); // // seg_R.add_point(xp, ap); // seg_L.add_point(xp, sp); // seg_R.build(); // seg_L.build(); // seg_R.set(xp, ap, 0); // seg_L.set(xp, sp, 0); // } // ll ans = 0; // for (auto i : ind) { // int xp = lower_bound(all(X2), X[i]) - X2.begin(); // int ap = lower_bound(all(add), X[i] + K * T[i]) - add.begin(); // int sp = lower_bound(all(sub), X[i] - K * T[i]) - sub.begin(); // ll r = seg_R.prod(xp, len(X2), 0, ap); // ll l = seg_L.prod(0, xp, sp, len(sub)); // ll ma = max(r, l) + C[i]; // chmax(ans, ma); // seg_R.set(xp, ap, ma); // seg_L.set(xp, sp, ma); // } // print(ans); // } // // int main() { // #ifndef INTERACTIVE // std::cin.tie(0)->sync_with_stdio(0); // #endif // // std::cout << std::fixed << std::setprecision(12); // int t; // t = 1; // // std::cin >> t; // while (t--) solve(); // return 0; // }