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#define PROBLEM "https://yukicoder.me/problems/no/2859" #include "my_template.hpp" #include "other/io.hpp" #include "ds/wavelet_matrix/wavelet_matrix_2d_range.hpp" #include "alg/monoid/max.hpp" #include "ds/segtree/segtree.hpp" void solve() { LL(N, K); VEC(ll, T, N); VEC(ll, X, N); VEC(ll, C, N); auto I = argsort(T); T = rearrange(T, I); X = rearrange(X, I); C = rearrange(C, I); vi A(N), B(N); FOR(i, N) A[i] = X[i] + K * T[i]; FOR(i, N) B[i] = K * T[i] - X[i]; Wavelet_Matrix_2D_Range<ll, 0, 0, SegTree<Monoid_Max<ll>>> seg(N, [&](int i) -> tuple<ll, ll, ll> { return {A[i], B[i], -infty<ll>}; }); ll ANS = 0; FOR(i, N) { if (abs(X[i]) > K * T[i]) continue; ll ans = 0; chmax(ans, seg.prefix_prod(-infty<ll>, A[i] + 1, B[i] + 1)); ans += C[i]; seg.set(i, ans); chmax(ANS, ans); } print(ANS); } signed main() { int T = 1; // INT(T); FOR(T) solve(); return 0; }
#line 1 "test/3_yukicoder/2859.test.cpp" #define PROBLEM "https://yukicoder.me/problems/no/2859" #line 1 "my_template.hpp" #if defined(LOCAL) #include <my_template_compiled.hpp> #else // https://codeforces.com/blog/entry/96344 #pragma GCC optimize("Ofast,unroll-loops") // いまの CF だとこれ入れると動かない? // #pragma GCC target("avx2,popcnt") #include <bits/stdc++.h> using namespace std; using ll = long long; using u8 = uint8_t; using u16 = uint16_t; using u32 = uint32_t; using u64 = uint64_t; using i128 = __int128; using u128 = unsigned __int128; using f128 = __float128; template <class T> constexpr T infty = 0; template <> constexpr int infty<int> = 1'010'000'000; template <> constexpr ll infty<ll> = 2'020'000'000'000'000'000; template <> constexpr u32 infty<u32> = infty<int>; template <> constexpr u64 infty<u64> = infty<ll>; template <> constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000; template <> constexpr double infty<double> = infty<ll>; template <> constexpr long double infty<long double> = infty<ll>; using pi = pair<ll, ll>; using vi = vector<ll>; template <class T> using vc = vector<T>; template <class T> using vvc = vector<vc<T>>; template <class T> using vvvc = vector<vvc<T>>; template <class T> using vvvvc = vector<vvvc<T>>; template <class T> using vvvvvc = vector<vvvvc<T>>; template <class T> using pq = priority_queue<T>; template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>; #define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__)) #define vvv(type, name, h, w, ...) vector<vector<vector<type>>> name(h, vector<vector<type>>(w, vector<type>(__VA_ARGS__))) #define vvvv(type, name, a, b, c, ...) \ vector<vector<vector<vector<type>>>> name(a, vector<vector<vector<type>>>(b, vector<vector<type>>(c, vector<type>(__VA_ARGS__)))) // https://trap.jp/post/1224/ #define FOR1(a) for (ll _ = 0; _ < ll(a); ++_) #define FOR2(i, a) for (ll i = 0; i < ll(a); ++i) #define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i) #define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c)) #define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i) #define overload4(a, b, c, d, e, ...) e #define overload3(a, b, c, d, ...) d #define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__) #define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__) #define FOR_subset(t, s) for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s))) #define all(x) x.begin(), x.end() #define len(x) ll(x.size()) #define elif else if #define eb emplace_back #define mp make_pair #define mt make_tuple #define fi first #define se second #define stoi stoll int popcnt(int x) { return __builtin_popcount(x); } int popcnt(u32 x) { return __builtin_popcount(x); } int popcnt(ll x) { return __builtin_popcountll(x); } int popcnt(u64 x) { return __builtin_popcountll(x); } int popcnt_sgn(int x) { return (__builtin_parity(x) & 1 ? -1 : 1); } int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); } int popcnt_sgn(ll x) { return (__builtin_parity(x) & 1 ? -1 : 1); } int popcnt_sgn(u64 x) { return (__builtin_parity(x) & 1 ? -1 : 1); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2) int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2) int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } template <typename T> T kth_bit(int k) { return T(1) << k; } template <typename T> bool has_kth_bit(T x, int k) { return x >> k & 1; } template <typename T> T floor(T a, T b) { return a / b - (a % b && (a ^ b) < 0); } template <typename T> T ceil(T x, T y) { return floor(x + y - 1, y); } template <typename T> T bmod(T x, T y) { return x - y * floor(x, y); } template <typename T> pair<T, T> divmod(T x, T y) { T q = floor(x, y); return {q, x - q * y}; } template <typename T, typename U> T SUM(const vector<U> &A) { T sm = 0; for (auto &&a: A) sm += a; return sm; } #define MIN(v) *min_element(all(v)) #define MAX(v) *max_element(all(v)) #define LB(c, x) distance((c).begin(), lower_bound(all(c), (x))) #define UB(c, x) distance((c).begin(), upper_bound(all(c), (x))) #define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit() template <typename T> T POP(deque<T> &que) { T a = que.front(); que.pop_front(); return a; } template <typename T> T POP(pq<T> &que) { T a = que.top(); que.pop(); return a; } template <typename T> T POP(pqg<T> &que) { T a = que.top(); que.pop(); return a; } template <typename T> T POP(vc<T> &que) { T a = que.back(); que.pop_back(); return a; } template <typename F> ll binary_search(F check, ll ok, ll ng, bool check_ok = true) { if (check_ok) assert(check(ok)); while (abs(ok - ng) > 1) { auto x = (ng + ok) / 2; (check(x) ? ok : ng) = x; } return ok; } template <typename F> double binary_search_real(F check, double ok, double ng, int iter = 100) { FOR(iter) { double x = (ok + ng) / 2; (check(x) ? ok : ng) = x; } return (ok + ng) / 2; } template <class T, class S> inline bool chmax(T &a, const S &b) { return (a < b ? a = b, 1 : 0); } template <class T, class S> inline bool chmin(T &a, const S &b) { return (a > b ? a = b, 1 : 0); } // ? は -1 vc<int> s_to_vi(const string &S, char first_char) { vc<int> A(S.size()); FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); } return A; } template <typename T, typename U> vector<T> cumsum(vector<U> &A, int off = 1) { int N = A.size(); vector<T> B(N + 1); FOR(i, N) { B[i + 1] = B[i] + A[i]; } if (off == 0) B.erase(B.begin()); return B; } // stable sort template <typename T> vector<int> argsort(const vector<T> &A) { vector<int> ids(len(A)); iota(all(ids), 0); sort(all(ids), [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); }); return ids; } // A[I[0]], A[I[1]], ... template <typename T> vc<T> rearrange(const vc<T> &A, const vc<int> &I) { vc<T> B(len(I)); FOR(i, len(I)) B[i] = A[I[i]]; return B; } template <typename T, typename... Vectors> void concat(vc<T> &first, const Vectors &... others) { vc<T> &res = first; (res.insert(res.end(), others.begin(), others.end()), ...); } #endif #line 1 "other/io.hpp" #define FASTIO #include <unistd.h> // https://judge.yosupo.jp/submission/21623 namespace fastio { static constexpr uint32_t SZ = 1 << 17; char ibuf[SZ]; char obuf[SZ]; char out[100]; // pointer of ibuf, obuf uint32_t pil = 0, pir = 0, por = 0; struct Pre { char num[10000][4]; constexpr Pre() : num() { for (int i = 0; i < 10000; i++) { int n = i; for (int j = 3; j >= 0; j--) { num[i][j] = n % 10 | '0'; n /= 10; } } } } constexpr pre; inline void load() { memcpy(ibuf, ibuf + pil, pir - pil); pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin); pil = 0; if (pir < SZ) ibuf[pir++] = '\n'; } inline void flush() { fwrite(obuf, 1, por, stdout); por = 0; } void rd(char &c) { do { if (pil + 1 > pir) load(); c = ibuf[pil++]; } while (isspace(c)); } void rd(string &x) { x.clear(); char c; do { if (pil + 1 > pir) load(); c = ibuf[pil++]; } while (isspace(c)); do { x += c; if (pil == pir) load(); c = ibuf[pil++]; } while (!isspace(c)); } template <typename T> void rd_real(T &x) { string s; rd(s); x = stod(s); } template <typename T> void rd_integer(T &x) { if (pil + 100 > pir) load(); char c; do c = ibuf[pil++]; while (c < '-'); bool minus = 0; if constexpr (is_signed<T>::value || is_same_v<T, i128>) { if (c == '-') { minus = 1, c = ibuf[pil++]; } } x = 0; while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; } if constexpr (is_signed<T>::value || is_same_v<T, i128>) { if (minus) x = -x; } } void rd(int &x) { rd_integer(x); } void rd(ll &x) { rd_integer(x); } void rd(i128 &x) { rd_integer(x); } void rd(u32 &x) { rd_integer(x); } void rd(u64 &x) { rd_integer(x); } void rd(u128 &x) { rd_integer(x); } void rd(double &x) { rd_real(x); } void rd(long double &x) { rd_real(x); } void rd(f128 &x) { rd_real(x); } template <class T, class U> void rd(pair<T, U> &p) { return rd(p.first), rd(p.second); } template <size_t N = 0, typename T> void rd_tuple(T &t) { if constexpr (N < std::tuple_size<T>::value) { auto &x = std::get<N>(t); rd(x); rd_tuple<N + 1>(t); } } template <class... T> void rd(tuple<T...> &tpl) { rd_tuple(tpl); } template <size_t N = 0, typename T> void rd(array<T, N> &x) { for (auto &d: x) rd(d); } template <class T> void rd(vc<T> &x) { for (auto &d: x) rd(d); } void read() {} template <class H, class... T> void read(H &h, T &... t) { rd(h), read(t...); } void wt(const char c) { if (por == SZ) flush(); obuf[por++] = c; } void wt(const string s) { for (char c: s) wt(c); } void wt(const char *s) { size_t len = strlen(s); for (size_t i = 0; i < len; i++) wt(s[i]); } template <typename T> void wt_integer(T x) { if (por > SZ - 100) flush(); if (x < 0) { obuf[por++] = '-', x = -x; } int outi; for (outi = 96; x >= 10000; outi -= 4) { memcpy(out + outi, pre.num[x % 10000], 4); x /= 10000; } if (x >= 1000) { memcpy(obuf + por, pre.num[x], 4); por += 4; } else if (x >= 100) { memcpy(obuf + por, pre.num[x] + 1, 3); por += 3; } else if (x >= 10) { int q = (x * 103) >> 10; obuf[por] = q | '0'; obuf[por + 1] = (x - q * 10) | '0'; por += 2; } else obuf[por++] = x | '0'; memcpy(obuf + por, out + outi + 4, 96 - outi); por += 96 - outi; } template <typename T> void wt_real(T x) { ostringstream oss; oss << fixed << setprecision(15) << double(x); string s = oss.str(); wt(s); } void wt(int x) { wt_integer(x); } void wt(ll x) { wt_integer(x); } void wt(i128 x) { wt_integer(x); } void wt(u32 x) { wt_integer(x); } void wt(u64 x) { wt_integer(x); } void wt(u128 x) { wt_integer(x); } void wt(double x) { wt_real(x); } void wt(long double x) { wt_real(x); } void wt(f128 x) { wt_real(x); } template <class T, class U> void wt(const pair<T, U> val) { wt(val.first); wt(' '); wt(val.second); } template <size_t N = 0, typename T> void wt_tuple(const T t) { if constexpr (N < std::tuple_size<T>::value) { if constexpr (N > 0) { wt(' '); } const auto x = std::get<N>(t); wt(x); wt_tuple<N + 1>(t); } } template <class... T> void wt(tuple<T...> tpl) { wt_tuple(tpl); } template <class T, size_t S> void wt(const array<T, S> val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) wt(' '); wt(val[i]); } } template <class T> void wt(const vector<T> val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) wt(' '); wt(val[i]); } } void print() { wt('\n'); } template <class Head, class... Tail> void print(Head &&head, Tail &&... tail) { wt(head); if (sizeof...(Tail)) wt(' '); print(forward<Tail>(tail)...); } // gcc expansion. called automaticall after main. void __attribute__((destructor)) _d() { flush(); } } // namespace fastio using fastio::read; using fastio::print; using fastio::flush; #if defined(LOCAL) #define SHOW(...) SHOW_IMPL(__VA_ARGS__, SHOW6, SHOW5, SHOW4, SHOW3, SHOW2, SHOW1)(__VA_ARGS__) #define SHOW_IMPL(_1, _2, _3, _4, _5, _6, NAME, ...) NAME #define SHOW1(x) print(#x, "=", (x)), flush() #define SHOW2(x, y) print(#x, "=", (x), #y, "=", (y)), flush() #define SHOW3(x, y, z) print(#x, "=", (x), #y, "=", (y), #z, "=", (z)), flush() #define SHOW4(x, y, z, w) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w)), flush() #define SHOW5(x, y, z, w, v) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v)), flush() #define SHOW6(x, y, z, w, v, u) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v), #u, "=", (u)), flush() #else #define SHOW(...) #endif #define INT(...) \ int __VA_ARGS__; \ read(__VA_ARGS__) #define LL(...) \ ll __VA_ARGS__; \ read(__VA_ARGS__) #define U32(...) \ u32 __VA_ARGS__; \ read(__VA_ARGS__) #define U64(...) \ u64 __VA_ARGS__; \ read(__VA_ARGS__) #define STR(...) \ string __VA_ARGS__; \ read(__VA_ARGS__) #define CHAR(...) \ char __VA_ARGS__; \ read(__VA_ARGS__) #define DBL(...) \ double __VA_ARGS__; \ read(__VA_ARGS__) #define VEC(type, name, size) \ vector<type> name(size); \ read(name) #define VV(type, name, h, w) \ vector<vector<type>> name(h, vector<type>(w)); \ read(name) void YES(bool t = 1) { print(t ? "YES" : "NO"); } void NO(bool t = 1) { YES(!t); } void Yes(bool t = 1) { print(t ? "Yes" : "No"); } void No(bool t = 1) { Yes(!t); } void yes(bool t = 1) { print(t ? "yes" : "no"); } void no(bool t = 1) { yes(!t); } void YA(bool t = 1) { print(t ? "YA" : "TIDAK"); } void TIDAK(bool t = 1) { YES(!t); } #line 4 "test/3_yukicoder/2859.test.cpp" #line 1 "ds/bit_vector.hpp" struct Bit_Vector { int n; bool prepared = 0; vc<pair<u64, u32>> dat; Bit_Vector(int n = 0) : n(n) { dat.assign((n + 127) >> 6, {0, 0}); } void set(int i) { assert(!prepared && (0 <= i && i < n)); dat[i >> 6].fi |= u64(1) << (i & 63); } void reset() { fill(all(dat), pair<u64, u32>{0, 0}); prepared = 0; } void build() { prepared = 1; FOR(i, len(dat) - 1) dat[i + 1].se = dat[i].se + popcnt(dat[i].fi); } // [0, k) 内の 1 の個数 bool operator[](int i) { return dat[i >> 6].fi >> (i & 63) & 1; } int count_prefix(int k, bool f = true) { assert(prepared); auto [a, b] = dat[k >> 6]; int ret = b + popcnt(a & ((u64(1) << (k & 63)) - 1)); return (f ? ret : k - ret); } int count(int L, int R, bool f = true) { return count_prefix(R, f) - count_prefix(L, f); } string to_string() { string ans; FOR(i, n) ans += '0' + (dat[i / 64].fi >> (i % 64) & 1); return ans; } }; #line 1 "ds/index_compression.hpp" template <typename T> struct Index_Compression_DISTINCT_SMALL { static_assert(is_same_v<T, int>); int mi, ma; vc<int> dat; vc<int> build(vc<int> X) { mi = 0, ma = -1; if (!X.empty()) mi = MIN(X), ma = MAX(X); dat.assign(ma - mi + 2, 0); for (auto& x: X) dat[x - mi + 1]++; FOR(i, len(dat) - 1) dat[i + 1] += dat[i]; for (auto& x: X) { x = dat[x - mi]++; } FOR_R(i, 1, len(dat)) dat[i] = dat[i - 1]; dat[0] = 0; return X; } int operator()(ll x) { return dat[clamp<ll>(x - mi, 0, ma - mi + 1)]; } }; template <typename T> struct Index_Compression_SAME_SMALL { static_assert(is_same_v<T, int>); int mi, ma; vc<int> dat; vc<int> build(vc<int> X) { mi = 0, ma = -1; if (!X.empty()) mi = MIN(X), ma = MAX(X); dat.assign(ma - mi + 2, 0); for (auto& x: X) dat[x - mi + 1] = 1; FOR(i, len(dat) - 1) dat[i + 1] += dat[i]; for (auto& x: X) { x = dat[x - mi]; } return X; } int operator()(ll x) { return dat[clamp<ll>(x - mi, 0, ma - mi + 1)]; } }; template <typename T> struct Index_Compression_SAME_LARGE { vc<T> dat; vc<int> build(vc<T> X) { vc<int> I = argsort(X); vc<int> res(len(X)); for (auto& i: I) { if (!dat.empty() && dat.back() == X[i]) { res[i] = len(dat) - 1; } else { res[i] = len(dat); dat.eb(X[i]); } } dat.shrink_to_fit(); return res; } int operator()(T x) { return LB(dat, x); } }; template <typename T> struct Index_Compression_DISTINCT_LARGE { vc<T> dat; vc<int> build(vc<T> X) { vc<int> I = argsort(X); vc<int> res(len(X)); for (auto& i: I) { res[i] = len(dat), dat.eb(X[i]); } dat.shrink_to_fit(); return res; } int operator()(T x) { return LB(dat, x); } }; template <typename T, bool SMALL> using Index_Compression_DISTINCT = typename std::conditional<SMALL, Index_Compression_DISTINCT_SMALL<T>, Index_Compression_DISTINCT_LARGE<T>>::type; template <typename T, bool SMALL> using Index_Compression_SAME = typename std::conditional<SMALL, Index_Compression_SAME_SMALL<T>, Index_Compression_SAME_LARGE<T>>::type; // SAME: [2,3,2] -> [0,1,0] // DISTINCT: [2,2,3] -> [0,2,1] // (x): lower_bound(X,x) をかえす template <typename T, bool SAME, bool SMALL> using Index_Compression = typename std::conditional<SAME, Index_Compression_SAME<T, SMALL>, Index_Compression_DISTINCT<T, SMALL>>::type; #line 2 "alg/monoid/add.hpp" template <typename E> struct Monoid_Add { using X = E; using value_type = X; static constexpr X op(const X &x, const X &y) noexcept { return x + y; } static constexpr X inverse(const X &x) noexcept { return -x; } static constexpr X power(const X &x, ll n) noexcept { return X(n) * x; } static constexpr X unit() { return X(0); } static constexpr bool commute = true; }; #line 4 "ds/wavelet_matrix/wavelet_matrix.hpp" // 静的メソッドinverseの存在をチェックするテンプレート template <typename, typename = std::void_t<>> struct has_inverse : std::false_type {}; template <typename T> struct has_inverse<T, std::void_t<decltype(T::inverse(std::declval<typename T::value_type>()))>> : std::true_type {}; struct Dummy_Data_Structure { using MX = Monoid_Add<bool>; void build(const vc<bool>& A) {} }; template <typename Y, bool SMALL_Y, typename SEGTREE = Dummy_Data_Structure> struct Wavelet_Matrix { using Mono = typename SEGTREE::MX; using T = typename Mono::value_type; static_assert(Mono::commute); int n, log, K; Index_Compression<Y, true, SMALL_Y> IDX; vc<Y> ItoY; vc<int> mid; vc<Bit_Vector> bv; vc<SEGTREE> seg; Wavelet_Matrix() {} Wavelet_Matrix(const vc<Y>& A) { build(A); } Wavelet_Matrix(const vc<Y>& A, vc<T>& SUM_Data) { build(A, SUM_Data); } template <typename F> Wavelet_Matrix(int n, F f) { build(n, f); } template <typename F> void build(int m, F f) { vc<Y> A(m); vc<T> S(m); for (int i = 0; i < m; ++i) tie(A[i], S[i]) = f(i); build(A, S); } void build(const vc<Y>& A) { build(A, vc<T>(len(A), Mono::unit())); } void build(const vc<Y>& A, vc<T> S) { n = len(A); vc<int> B = IDX.build(A); K = 0; for (auto& x: B) chmax(K, x + 1); ItoY.resize(K); FOR(i, n) ItoY[B[i]] = A[i]; log = 0; while ((1 << log) < K) ++log; mid.resize(log), bv.assign(log, Bit_Vector(n)); vc<int> B0(n), B1(n); vc<T> S0(n), S1(n); seg.resize(log + 1); seg[log].build(S); for (int d = log - 1; d >= 0; --d) { int p0 = 0, p1 = 0; for (int i = 0; i < n; ++i) { bool f = (B[i] >> d & 1); if (!f) { B0[p0] = B[i], S0[p0] = S[i], p0++; } if (f) { bv[d].set(i), B1[p1] = B[i], S1[p1] = S[i], p1++; } } swap(B, B0), swap(S, S0); move(B1.begin(), B1.begin() + p1, B.begin() + p0); move(S1.begin(), S1.begin() + p1, S.begin() + p0); mid[d] = p0, bv[d].build(), seg[d].build(S); } } // [L,R) x [0,y) int prefix_count(int L, int R, Y y) { int p = IDX(y); if (L == R || p == 0) return 0; if (p == K) return R - L; int cnt = 0; for (int d = log - 1; d >= 0; --d) { int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0); int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0; if (p >> d & 1) cnt += r0 - l0, L = l1, R = r1; if (!(p >> d & 1)) L = l0, R = r0; } return cnt; } // [L,R) x [y1,y2) int count(int L, int R, Y y1, Y y2) { return prefix_count(L, R, y2) - prefix_count(L, R, y1); } // [L,R) x [0,y) pair<int, T> prefix_count_and_prod(int L, int R, Y y) { int p = IDX(y); if (p == 0) return {0, Mono::unit()}; if (p == K) return {R - L, seg[log].prod(L, R)}; int cnt = 0; T t = Mono::unit(); for (int d = log - 1; d >= 0; --d) { int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0); int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0; if (p >> d & 1) { cnt += r0 - l0, t = Mono::op(t, seg[d].prod(l0, r0)), L = l1, R = r1; } if (!(p >> d & 1)) L = l0, R = r0; } return {cnt, t}; } // [L,R) x [y1,y2) pair<int, T> count_and_prod(int L, int R, Y y1, Y y2) { if constexpr (has_inverse<Mono>::value) { auto [c1, t1] = prefix_count_and_prod(L, R, y1); auto [c2, t2] = prefix_count_and_prod(L, R, y2); return {c2 - c1, Mono::op(Mono::inverse(t1), t2)}; } int lo = IDX(y1), hi = IDX(y2), cnt = 0; T t = Mono::unit(); auto dfs = [&](auto& dfs, int d, int L, int R, int a, int b) -> void { assert(b - a == (1 << d)); if (hi <= a || b <= lo) return; if (lo <= a && b <= hi) { cnt += R - L, t = Mono::op(t, seg[d].prod(L, R)); return; } --d; int c = (a + b) / 2; int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0); int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0; dfs(dfs, d, l0, r0, a, c), dfs(dfs, d, l1, r1, c, b); }; dfs(dfs, log, L, R, 0, 1 << log); return {cnt, t}; } // [L,R) x [y1,y2) T prefix_prod(int L, int R, Y y) { return prefix_count_and_prod(L, R, y).se; } // [L,R) x [y1,y2) T prod(int L, int R, Y y1, Y y2) { return count_and_prod(L, R, y1, y2).se; } T prod_all(int L, int R) { return seg[log].prod(L, R); } Y kth(int L, int R, int k) { assert(0 <= k && k < R - L); int p = 0; for (int d = log - 1; d >= 0; --d) { int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0); int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0; if (k < r0 - l0) { L = l0, R = r0; } else { k -= r0 - l0, L = l1, R = r1, p |= 1 << d; } } return ItoY[p]; } // y 以上最小 OR infty<Y> Y next(int L, int R, Y y) { int k = IDX(y); int p = K; auto dfs = [&](auto& dfs, int d, int L, int R, int a, int b) -> void { if (p <= a || L == R || b <= k) return; if (d == 0) { chmin(p, a); return; } --d; int c = (a + b) / 2; int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0); int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0; dfs(dfs, d, l0, r0, a, c), dfs(dfs, d, l1, r1, c, b); }; dfs(dfs, log, L, R, 0, 1 << log); return (p == K ? infty<Y> : ItoY[p]); } // y 以下最大 OR -infty<T> Y prev(int L, int R, Y y) { int k = IDX(y + 1); int p = -1; auto dfs = [&](auto& dfs, int d, int L, int R, int a, int b) -> void { if (b - 1 <= p || L == R || k <= a) return; if (d == 0) { chmax(p, a); return; } --d; int c = (a + b) / 2; int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0); int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0; dfs(dfs, d, l1, r1, c, b), dfs(dfs, d, l0, r0, a, c); }; dfs(dfs, log, L, R, 0, 1 << log); return (p == -1 ? -infty<Y> : ItoY[p]); } Y median(bool UPPER, int L, int R) { assert(0 <= L && L < R && R <= n); int k = (UPPER ? (R - L) / 2 : (R - L - 1) / 2); return kth(L, R, k); } pair<Y, T> kth_value_and_prod(int L, int R, int k) { assert(0 <= k && k <= R - L); if (k == R - L) return {infty<Y>, seg[log].prod(L, R)}; int p = 0; T t = Mono::unit(); for (int d = log - 1; d >= 0; --d) { int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0); int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0; if (k < r0 - l0) { L = l0, R = r0; } else { t = Mono::op(t, seg[d].prod(l0, r0)), k -= r0 - l0, L = l1, R = r1, p |= 1 << d; } } t = Mono::op(t, seg[0].prod(L, L + k)); return {ItoY[p], t}; } T prod_index_range(int L, int R, int k1, int k2) { static_assert(has_inverse<Mono>::value); T t1 = kth_value_and_prod(L, R, k1).se; T t2 = kth_value_and_prod(L, R, k2).se; return Mono::op(Mono::inverse(t1), t2); } // [L,R) x [0,y) での check(cnt, prod) が true となる最大の (cnt,prod) template <typename F> pair<int, T> max_right(F check, int L, int R) { int cnt = 0; T t = Mono::unit(); assert(check(0, Mono::unit())); if (check(R - L, seg[log].prod(L, R))) { return {R - L, seg[log].prod(L, R)}; } for (int d = log - 1; d >= 0; --d) { int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0); int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0; int cnt1 = cnt + r0 - l0; T t1 = Mono::op(t, seg[d].prod(l0, r0)); if (check(cnt1, t1)) { cnt = cnt1, t = t1, L = l1, R = r1; } else { L = l0, R = r0; } } return {cnt, t}; } void set(int i, T t) { assert(0 <= i && i < n); int L = i, R = i + 1; seg[log].set(L, t); for (int d = log - 1; d >= 0; --d) { int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0); int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0; if (l0 < r0) L = l0, R = r0; if (l0 == r0) L = l1, R = r1; seg[d].set(L, t); } } void multiply(int i, T t) { assert(0 <= i && i < n); int L = i, R = i + 1; seg[log].multiply(L, t); for (int d = log - 1; d >= 0; --d) { int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0); int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0; if (l0 < r0) L = l0, R = r0; if (l0 == r0) L = l1, R = r1; seg[d].multiply(L, t); } } void add(int i, T t) { multiply(i, t); } }; #line 2 "ds/wavelet_matrix/wavelet_matrix_2d_range.hpp" template <typename XY, bool SMALL_X, bool SMALL_Y, typename SEGTREE = Dummy_Data_Structure> struct Wavelet_Matrix_2D_Range { // 点群を X 昇順に並べる. Wavelet_Matrix<XY, SMALL_Y, SEGTREE> WM; using Mono = typename SEGTREE::MX; using T = typename Mono::value_type; static_assert(Mono::commute); Index_Compression<XY, false, SMALL_X> IDX_X; int n; vc<int> new_idx; template <typename F> Wavelet_Matrix_2D_Range(int n, F f) { build(n, f); } template <typename F> void build(int m, F f) { n = m; vc<XY> X(n), Y(n); vc<T> S(n); FOR(i, n) { auto tmp = f(i); X[i] = get<0>(tmp), Y[i] = get<1>(tmp), S[i] = get<2>(tmp); } new_idx = IDX_X.build(X); vc<int> I(n); FOR(i, n) I[new_idx[i]] = i; Y = rearrange(Y, I); S = rearrange(S, I); WM.build(Y, S); } int count(XY x1, XY x2, XY y1, XY y2) { return WM.count(IDX_X(x1), IDX_X(x2), y1, y2); } // [L,R) x [-inf,y) pair<int, T> prefix_count_and_prod(XY x1, XY x2, XY y) { return WM.prefix_count_and_prod(IDX_X(x1), IDX_X(x2), y); } // [L,R) x [y1,y2) pair<int, T> count_and_prod(XY x1, XY x2, XY y1, XY y2) { return WM.count_and_prod(IDX_X(x1), IDX_X(x2), y1, y2); } // [L,R) x [-inf,inf) T prod_all(XY x1, XY x2) { return WM.prod_all(IDX_X(x1), IDX_X(x2)); } // [L,R) x [-inf,y) T prefix_prod(XY x1, XY x2, XY y) { return WM.prefix_prod(IDX_X(x1), IDX_X(x2), y); } // [L,R) x [y1,y2) T prod(XY x1, XY x2, XY y1, XY y2) { return WM.prod(IDX_X(x1), IDX_X(x2), y1, y2); } // [L,R) x [-inf,y) での check(cnt, prod) が true となる最大の (cnt,prod) template <typename F> pair<int, T> max_right(F check, XY x1, XY x2) { return WM.max_right(check, IDX_X(x1), IDX_X(x2)); } // i は最初に渡したインデックス void set(int i, T t) { WM.set(new_idx[i], t); } // i は最初に渡したインデックス void multiply(int i, T t) { WM.multiply(new_idx[i], t); } void add(int i, T t) { WM.multiply(new_idx[i], t); } }; #line 2 "alg/monoid/max.hpp" template <typename E> struct Monoid_Max { using X = E; using value_type = X; static constexpr X op(const X &x, const X &y) noexcept { return max(x, y); } static constexpr X unit() { return -infty<E>; } static constexpr bool commute = true; }; #line 2 "ds/segtree/segtree.hpp" template <class Monoid> struct SegTree { using MX = Monoid; using X = typename MX::value_type; using value_type = X; vc<X> dat; int n, log, size; SegTree() {} SegTree(int n) { build(n); } template <typename F> SegTree(int n, F f) { build(n, f); } SegTree(const vc<X>& v) { build(v); } void build(int m) { build(m, [](int i) -> X { return MX::unit(); }); } void build(const vc<X>& v) { build(len(v), [&](int i) -> X { return v[i]; }); } template <typename F> void build(int m, F f) { n = m, log = 1; while ((1 << log) < n) ++log; size = 1 << log; dat.assign(size << 1, MX::unit()); FOR(i, n) dat[size + i] = f(i); FOR_R(i, 1, size) update(i); } X get(int i) { return dat[size + i]; } vc<X> get_all() { return {dat.begin() + size, dat.begin() + size + n}; } void update(int i) { dat[i] = Monoid::op(dat[2 * i], dat[2 * i + 1]); } void set(int i, const X& x) { assert(i < n); dat[i += size] = x; while (i >>= 1) update(i); } void multiply(int i, const X& x) { assert(i < n); i += size; dat[i] = Monoid::op(dat[i], x); while (i >>= 1) update(i); } X prod(int L, int R) { assert(0 <= L && L <= R && R <= n); X vl = Monoid::unit(), vr = Monoid::unit(); L += size, R += size; while (L < R) { if (L & 1) vl = Monoid::op(vl, dat[L++]); if (R & 1) vr = Monoid::op(dat[--R], vr); L >>= 1, R >>= 1; } return Monoid::op(vl, vr); } X prod_all() { return dat[1]; } template <class F> int max_right(F check, int L) { assert(0 <= L && L <= n && check(Monoid::unit())); if (L == n) return n; L += size; X sm = Monoid::unit(); do { while (L % 2 == 0) L >>= 1; if (!check(Monoid::op(sm, dat[L]))) { while (L < size) { L = 2 * L; if (check(Monoid::op(sm, dat[L]))) { sm = Monoid::op(sm, dat[L++]); } } return L - size; } sm = Monoid::op(sm, dat[L++]); } while ((L & -L) != L); return n; } template <class F> int min_left(F check, int R) { assert(0 <= R && R <= n && check(Monoid::unit())); if (R == 0) return 0; R += size; X sm = Monoid::unit(); do { --R; while (R > 1 && (R % 2)) R >>= 1; if (!check(Monoid::op(dat[R], sm))) { while (R < size) { R = 2 * R + 1; if (check(Monoid::op(dat[R], sm))) { sm = Monoid::op(dat[R--], sm); } } return R + 1 - size; } sm = Monoid::op(dat[R], sm); } while ((R & -R) != R); return 0; } // prod_{l<=i<r} A[i xor x] X xor_prod(int l, int r, int xor_val) { static_assert(Monoid::commute); X x = Monoid::unit(); for (int k = 0; k < log + 1; ++k) { if (l >= r) break; if (l & 1) { x = Monoid::op(x, dat[(size >> k) + ((l++) ^ xor_val)]); } if (r & 1) { x = Monoid::op(x, dat[(size >> k) + ((--r) ^ xor_val)]); } l /= 2, r /= 2, xor_val /= 2; } return x; } }; #line 8 "test/3_yukicoder/2859.test.cpp" void solve() { LL(N, K); VEC(ll, T, N); VEC(ll, X, N); VEC(ll, C, N); auto I = argsort(T); T = rearrange(T, I); X = rearrange(X, I); C = rearrange(C, I); vi A(N), B(N); FOR(i, N) A[i] = X[i] + K * T[i]; FOR(i, N) B[i] = K * T[i] - X[i]; Wavelet_Matrix_2D_Range<ll, 0, 0, SegTree<Monoid_Max<ll>>> seg(N, [&](int i) -> tuple<ll, ll, ll> { return {A[i], B[i], -infty<ll>}; }); ll ANS = 0; FOR(i, N) { if (abs(X[i]) > K * T[i]) continue; ll ans = 0; chmax(ans, seg.prefix_prod(-infty<ll>, A[i] + 1, B[i] + 1)); ans += C[i]; seg.set(i, ans); chmax(ANS, ans); } print(ANS); } signed main() { int T = 1; // INT(T); FOR(T) solve(); return 0; }