#pragma region template #pragma GCC optimize("Ofast") #include using namespace std; using ll=long long; #define overload2(a,b,c,...) c #define overload3(a,b,c,d,...) d #define overload4(a,b,c,d,e,...) e #define overload5(a,b,c,d,e,f,...) f #define TYPE1(T) template #define TYPE2(T,U) template #define TYPE(...) overload2(__VA_ARGS__,TYPE2,TYPE1)(__VA_ARGS__) #define TYPES1(T) template #define TYPES2(H,T) template #define TYPES(...) overload2(__VA_ARGS__,TYPES2,TYPES1)(__VA_ARGS__) #define REP4(i,s,n,d) for(int i=(s);i<(n);i+=(d)) #define REP3(i,s,n) REP4(i,s,n,1) #define REP2(i,n) REP3(i,0,n) #define REP1(n) REP2(tomato,n) #define REP(...) overload4(__VA_ARGS__,REP4,REP3,REP2,REP1)(__VA_ARGS__) #define RREP4(i,n,s,d) for(int i=(n)-1;i>=(s);i-=(d)) #define RREP3(i,n,s) RREP4(i,n,s,1) #define RREP2(i,n) RREP3(i,n,0) #define RREP1(n) RREP2(tomato,n) #define RREP(...) overload4(__VA_ARGS__,RREP4,RREP3,RREP2,RREP1)(__VA_ARGS__) #define AFOR4(a,b,c,d,v) for(auto&[a,b,c,d]:v) #define AFOR3(a,b,c,v) for(auto&[a,b,c]:v) #define AFOR2(a,b,v) for(auto&[a,b]:v) #define AFOR1(a,v) for(auto&a:v) #define AFOR(...) overload5(__VA_ARGS__,AFOR4,AFOR3,AFOR2,AFOR1)(__VA_ARGS__) #define CFOR4(a,b,c,d,v) for(const auto&[a,b,c,d]:v) #define CFOR3(a,b,c,v) for(const auto&[a,b,c]:v) #define CFOR2(a,b,v) for(const auto&[a,b]:v) #define CFOR1(a,v) for(const auto&a:v) #define CFOR(...) overload5(__VA_ARGS__,CFOR4,CFOR3,CFOR2,CFOR1)(__VA_ARGS__) #define PFOR(v) for(bool f=true; (f ? exchange(f,false) : next_permutation(ALL(v)));) TYPES(T) void input(T&... a){ (cin>>...>>a); } #define DECLARE(T,...) T __VA_ARGS__;input(__VA_ARGS__); #define INT(...) DECLARE(int,__VA_ARGS__) #define STR(...) DECLARE(string,__VA_ARGS__) #define LL(...) DECLARE(long long,__VA_ARGS__) #define CHR(...) DECLARE(char,__VA_ARGS__) #define DBL(...) DECLARE(double,__VA_ARGS__) #define VI(n,v) vector v(n);cin>>v; #define VLL(n,v) vector v(n);cin>>v; #define VS(n,s) vector s(n);cin>>s; TYPE(T) istream&operator>>(istream&is,vector&v){ for(auto&a:v)cin>>a; return is; } TYPE(T) ostream&operator<<(ostream&os,const vector&v){ if(&os==&cerr)os<<"["; REP(i,v.size()){ os<>(istream&is,pair&p){ cin>>p.first>>p.second; return is; } #ifdef __DEBUG #include #else #define debug(...) void(0) #endif void print(){ cout << '\n'; } TYPES(T,Ts) void print(const T& a,const Ts&... b){ cout< constexpr T infty = 0; template <> constexpr int infty = 1'000'000'000; template <> constexpr ll infty = ll(infty) * infty * 2; template <> constexpr u32 infty = infty; template <> constexpr u64 infty = infty; template <> constexpr i128 infty = i128(infty) * infty; template <> constexpr double infty = infty; template <> constexpr long double infty = infty; using pi = pair; using vi = vector; template using vc = vector; template using vvc = vector>; template using vvvc = vector>; template using vvvvc = vector>; template using vvvvvc = vector>; template using pq = priority_queue; template using pqg = priority_queue, greater>; #define vv(type, name, h, ...) \ vector> name(h, vector(__VA_ARGS__)) #define vvv(type, name, h, w, ...) \ vector>> name( \ h, vector>(w, vector(__VA_ARGS__))) #define vvvv(type, name, a, b, c, ...) \ vector>>> name( \ a, vector>>( \ b, vector>(c, vector(__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); } // (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 T ceil(T x, U y) { return (x > 0 ? (x + y - 1) / y : x / y); } template T floor(T x, U y) { return (x > 0 ? x / y : (x - y + 1) / y); } template pair divmod(T x, U y) { T q = floor(x, y); return {q, x - q * y}; } template T SUM(const vector &A) { T sum = 0; for (auto &&a: A) sum += a; return sum; } #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 T POP(deque &que) { T a = que.front(); que.pop_front(); return a; } template T POP(pq &que) { T a = que.top(); que.pop(); return a; } template T POP(pqg &que) { assert(!que.empty()); T a = que.top(); que.pop(); return a; } template T POP(vc &que) { assert(!que.empty()); T a = que.back(); que.pop_back(); return a; } template 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; tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x)); } return ok; } template double binary_search_real(F check, double ok, double ng, int iter = 100) { FOR(iter) { double x = (ok + ng) / 2; tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x)); } return (ok + ng) / 2; } 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); } // ? は -1 vc s_to_vi(const string &S, char first_char) { vc A(S.size()); FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); } return A; } template vector cumsum(vector &A, int off = 1) { int N = A.size(); vector 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 vector argsort(const vector &A) { vector 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 vc rearrange(const vc &A, const vc &I) { vc B(len(I)); FOR(i, len(I)) B[i] = A[I[i]]; return B; } #line 1 "convex/dynamic_lichao.hpp" // 直線追加かつ非永続なら空間 Q でよい。 // 関数は ll -> T。[L, R) 上 f が overflow しないように注意。 // evaluate を書き変えると、totally monotone な関数群にも使える template struct Dynamic_LiChao_Tree { using FUNC = pair; vc funcs; static inline T evaluate(FUNC &f, ll x) { return f.fi * x + f.se; } struct Node { int fid; Node *l, *r; }; Node *pool; int pid; ll L, R; using np = Node *; Dynamic_LiChao_Tree(ll L, ll R) : pid(0), L(L), R(R) { pool = new Node[NODES]; } void reset() { funcs.clear(); pid = 0; } np new_root() { return nullptr; } np new_node() { pool[pid].fid = -1; pool[pid].l = nullptr, pool[pid].r = nullptr; return &(pool[pid++]); } np add_line(np root, FUNC f) { int fid = len(funcs); funcs.eb(f); if (!root) root = new_node(); return add_line_rec(root, fid, L, R); } // [xl, xr) np add_segment(np root, ll xl, ll xr, FUNC f) { int fid = len(funcs); funcs.eb(f); if (!root) root = new_node(); return add_segment_rec(root, xl, xr, fid, L, R); } // (値・関数番号) pair query(np root, ll x) { assert(L <= x && x < R); if (!root) { if (MINIMIZE) return {infty, -1}; if (!MINIMIZE) return {-infty, -1}; } return query_rec(root, x, L, R); } private: np copy_node(Node *c) { if (!c || !PERSISTENT) return c; pool[pid].fid = c->fid; pool[pid].l = c->l, pool[pid].r = c->r; return &(pool[pid++]); } inline T evaluate_inner(int fid, ll x) { if (fid == -1) { return (MINIMIZE ? infty : -infty); }; return evaluate(funcs[fid], x); } np add_segment_rec(np c, ll xl, ll xr, int fid, ll node_l, ll node_r) { chmax(xl, node_l), chmin(xr, node_r); if (xl >= xr) return c; if (node_l < xl || xr < node_r) { c = copy_node(c); ll node_m = (node_l + node_r) / 2; if (!c->l) c->l = new_node(); if (!c->r) c->r = new_node(); c->l = add_segment_rec(c->l, xl, xr, fid, node_l, node_m); c->r = add_segment_rec(c->r, xl, xr, fid, node_m, node_r); return c; } return add_line_rec(c, fid, node_l, node_r); } np add_line_rec(np c, int fid, ll node_l, ll node_r) { int gid = c->fid; T fl = evaluate_inner(fid, node_l), fr = evaluate_inner(fid, node_r - 1); T gl = evaluate_inner(gid, node_l), gr = evaluate_inner(gid, node_r - 1); bool bl = (MINIMIZE ? fl < gl : fl > gl); bool br = (MINIMIZE ? fr < gr : fr > gr); if (bl && br) { c = copy_node(c); c->fid = fid; return c; } if (!bl && !br) { return c; } c = copy_node(c); ll node_m = (node_l + node_r) / 2; auto fm = evaluate_inner(fid, node_m), gm = evaluate_inner(gid, node_m); bool bm = (MINIMIZE ? fm < gm : fm > gm); if (bm) { c->fid = fid; if (bl) { if (!c->r) c->r = new_node(); c->r = add_line_rec(c->r, gid, node_m, node_r); } else { if (!c->l) c->l = new_node(); c->l = add_line_rec(c->l, gid, node_l, node_m); } } if (!bm) { if (!bl) { if (!c->r) c->r = new_node(); c->r = add_line_rec(c->r, fid, node_m, node_r); } else { if (!c->l) c->l = new_node(); c->l = add_line_rec(c->l, fid, node_l, node_m); } } return c; } pair query_rec(np c, ll x, ll node_l, ll node_r) { int fid = c->fid; pair res = {evaluate_inner(fid, x), fid}; ll node_m = (node_l + node_r) / 2; if (x < node_m && c->l) { pair res1 = query_rec(c->l, x, node_l, node_m); res = (MINIMIZE ? min(res, res1) : max(res, res1)); } if (x >= node_m && c->r) { pair res1 = query_rec(c->r, x, node_m, node_r); res = (MINIMIZE ? min(res, res1) : max(res, res1)); } return res; } }; #include using namespace atcoder; int main(){ ios::sync_with_stdio(false); cin.tie(nullptr); INT(n,m); VLL(n,a); VLL(m,b); VLL(m,c); vi ab(n+m); REP(i,n)ab[i]=a[i]; REP(j,m)ab[n+j]=b[j]; Dynamic_LiChao_Tree X(-infty, infty); using np=decltype(X)::np; np root = X.new_root(); root = X.add_segment(root,0,1,{1,0}); auto z=z_algorithm(ab); REP(j,m){ auto [fval,fid]=X.query(root,j); debug(j,fval,fid); if(fid==-1)continue; int r=min(z[n+j],n); debug(r); if(r==0)continue; root = X.add_segment(root,j+1,j+r+1,{c[j],fval-j*c[j]}); } auto [fval,fid]=X.query(root,m); if(fid==-1)cout<<-1<<'\n'; else cout<