#include // clang-format off std::ostream&operator<<(std::ostream&os,std::int8_t x){return os<<(int)x;} std::ostream&operator<<(std::ostream&os,std::uint8_t x){return os<<(int)x;} std::ostream&operator<<(std::ostream&os,const __int128_t &v){if(!v)os<<"0";__int128_t tmp=v<0?(os<<"-",-v):v;std::string s;while(tmp)s+='0'+(tmp%10),tmp/=10;return std::reverse(s.begin(),s.end()),os<std::ostream &operator<<(std::ostream&os,const std::pair&x){return os<<"("<std::ostream &operator<<(std::ostream&os,const std::vector&vec){os<<'[';for(int _=0,__= vec.size();_<__;++_)os<<(_ ?", ":"")<std::ostream &operator<<(std::ostream&os,const std::set&s){os<<'{';int _=0;for(const auto &x:s)os<<(_++ ? ", " : "")<std::ostream&operator<<(std::ostream &os,const std::array &arr) {os<<'['<void print(std::ostream&os,const Tup &x,std::index_sequence){(void)(int[]){(os<(x)<<", ",0)...};} templatestd::ostream &operator<<(std::ostream&os,const std::tuple &x) {static constexpr std::size_t N = sizeof...(Args);os<<"(";if constexpr(N>=2)print(os,x,std::make_index_sequence());return os<(x)<<")";} const std::string COLOR_RESET="\033[0m",BRIGHT_GREEN="\033[1;32m",BRIGHT_RED="\033[1;31m",BRIGHT_CYAN="\033[1;36m",NORMAL_CROSSED="\033[0;9;37m",ITALIC="\033[3m",BOLD="\033[1m",RED_BACKGROUND="\033[1;41m",NORMAL_FAINT="\033[0;2m"; #define func_LINE_FILE NORMAL_FAINT<<" in "<"< auto compress(std::vector &v) { return std::sort(v.begin(), v.end()), v.erase(std::unique(v.begin(), v.end()), v.end()), [&v](T x) { return std::lower_bound(v.begin(), v.end(), x) - v.begin(); }; } class PiecewiseLinearConvexfunction { public: using i64= long long; using i128= __int128_t; static constexpr i64 INF= 1ll << 60; template static inline std::string str(Int x) { if (x >= INF) return "inf"; if (x <= -INF) return "-inf"; std::stringstream ss; ss << x; return ss.str(); } struct Node { Node *ch[2]= {nullptr, nullptr}, *par= nullptr; i64 dat[2]= {0, 0}, laz[2]= {0, 0}; }; friend std::ostream &operator<<(std::ostream &os, Node *t) { if (!t) return os << "nullptr"; return os << "{dat[2]:(" << str(t->dat[0]) << "," << str(t->dat[1]) << "), laz[2]:(" << str(t->laz[0]) << "," << str(t->laz[1]) << ") }"; } // friend std::ostream &operator<<(std::ostream &os, Node *t) { // if (!t) return os << "nullptr"; // return os << "(" << str(t->dat[0]) << "," << str(t->dat[1]) << ")"; // } static inline void propagate(Node *t, const i64 x[2]) { if (t) t->dat[0]+= x[0], t->laz[0]+= x[0], t->dat[1]+= x[1], t->laz[1]+= x[1]; } static inline void push(Node *t) { propagate(t->ch[0], t->laz), propagate(t->ch[1], t->laz), t->laz[0]= t->laz[1]= 0; } static inline int dir(Node *&t) { if (t->par) { if (t->par->ch[0] == t) return 0; if (t->par->ch[1] == t) return 1; } return 2; } static inline void rot(Node *t) { Node *p= t->par; int d= dir(t); if ((p->ch[d]= t->ch[!d])) p->ch[d]->par= p; t->ch[!d]= p, t->par= p->par; if ((d= dir(p)) < 2) p->par->ch[d]= t; p->par= t; } static inline void splay(Node *t) { for (int t_d= dir(t), p_d; t_d < 2; rot(t), t_d= dir(t)) if ((p_d= dir(t->par)) < 2) rot(t_d == p_d ? t->par : t); } static inline void bin_search(Node *&t, i64 k, bool b) { for (Node *s;; t= s) { push(t); i64 tmp= t->dat[b]; if (tmp == k) break; if (s= t->ch[tmp < k]; !s) break; } splay(t); } static inline i128 eval(Node *t, i64 x, i64 &p) { if (!t) return 0; push(t); i128 ret= eval(t->ch[0], x, p); if (i64 tmp= x - t->dat[0]; tmp > 0) { ret+= i128(tmp) * (t->dat[1] - p); p= t->dat[1]; ret+= eval(t->ch[1], x, p); } return ret; } static void dump(Node *t, std::vector &vec) { if (!t) return; push(t); dump(t->ch[0], vec); vec.emplace_back(t); dump(t->ch[1], vec); } static int size(Node *t) { if (!t) return 0; return size(t->ch[0]) + size(t->ch[1]) + 1; } static int depth(Node *t) { if (!t) return 0; return std::max(depth(t->ch[0]), depth(t->ch[1])) + 1; } static inline void debugoutput(Node *t, int d) { if (!t) return; // push(t); debugoutput(t->ch[0], d + 1); for (int i= 0; i < d; ++i) std::cerr << " "; std::cerr << "■ " << t << '\n'; debugoutput(t->ch[1], d + 1); } Node *root; i64 A; i128 C; public: std::vector dump() { std::vector vec; dump(root, vec); return vec; } int depth() { return depth(root); } int size() { return size(root); } void debugoutput() { debugoutput(root, 0); } // f(x) := 0 PiecewiseLinearConvexfunction(): A(0), C(0) { root= new Node, root->dat[0]= -INF * 2, root->dat[1]= 0; } // f(x) := 0 if x == 0 else ∞ PiecewiseLinearConvexfunction(int a): A(-INF * 2), C(0) { root= new Node, root->dat[0]= 0, root->dat[1]= INF * 2; } // f(x) + c void add_const(i64 c) { C+= c; } // f(x) + ax+c void add_linear(i64 a, i64 c= 0) { A+= a, C+= c; i64 aa[2]= {0, a}; propagate(root, aa); } // f(x-a) void shift(i64 a) { C-= i128(A) * a; i64 aa[2]= {a, 0}; propagate(root, aa); } // f(x) + a * max{x, 0} void add_relu(i64 a) { i64 aa[2]= {0, a}; bin_search(root, 0, 0); if (i64 tmp= root->dat[0]; tmp) { if (tmp > 0 && !root->ch[0]) { Node *t= new Node; t->dat[1]= A; t->ch[1]= root, root->par= t; root= t; } else { if (tmp > 0) { Node *s= root->ch[0]; for (;; s= s->ch[1]) if (push(s); !s->ch[1]) break; splay(s), root= s; } Node *t= new Node; t->dat[1]= root->dat[1]; t->ch[1]= root->ch[1]; if (t->ch[1]) t->ch[1]->par= t; root->ch[1]= nullptr; t->ch[0]= root, root->par= t; root= t; } } Node *l= root->ch[0]; root->ch[0]= nullptr; propagate(root, aa); push(root), root->ch[0]= l; } // min_{y∈[0,a]}{f(x-y)} void chmin_sliding_window(i64 a) { i64 aa[2]= {a, 0}; bin_search(root, 0, 1); if (i64 tmp= root->dat[1]; tmp) { if (tmp > 0 && !root->ch[0]) { Node *t= new Node; t->dat[0]= -INF; t->ch[1]= root, root->par= t; root= t; } else { if (tmp > 0) { Node *s= root->ch[0]; for (;; s= s->ch[1]) if (push(s); !s->ch[1]) break; splay(s), root= s; } Node *t= new Node; t->dat[0]= root->dat[0]; t->ch[1]= root->ch[1]; if (t->ch[1]) t->ch[1]->par= t; root->ch[1]= nullptr; t->ch[0]= root, root->par= t; root= t; } } Node *l= root->ch[0]; root->ch[0]= nullptr; propagate(root, aa); push(root), root->ch[0]= l; } // min_{y<=x} f(y) void cumulative_chmin() { bin_search(root, 0, 1); if (i64 tmp= root->dat[1]; tmp < 0) { Node *t= root->ch[1]; for (;; t= t->ch[0]) if (push(t); !t->ch[0]) break; splay(t), root= t; } root->ch[1]= nullptr, root->dat[1]= 0; } // f(x) + a * min{x,0} + b * max{x,0} void add_ax_bx(i64 a, i64 b) { add_linear(a), add_relu(b - a); } // f(x) + a * min{x-c,0} + b * max{x-c,0} void add_ax_bx_c(i64 a, i64 b, i64 c) { shift(-c), add_ax_bx(a, b), shift(c); } // f(x) + a * |x-c| void add_abs(i64 a, i64 c) { add_ax_bx_c(-a, a, c); } // f(x) i128 eval(i64 x) { i64 p= A; return eval(root, x, p) + i128(A) * x + C; } std::array argmin() { std::array ret; bin_search(root, 0, 1); if (i64 tmp= root->dat[1]; tmp <= 0) { Node *t= root->ch[1]; for (;; t= t->ch[0]) if (push(t); !t->ch[0]) break; if (tmp) ret= {t->dat[0], t->dat[0]}; else ret= {root->dat[0], t->dat[0]}; splay(t), root= t; } else if (tmp > 0) ret= {root->dat[0], root->dat[0]}; return ret; } i128 min() { return eval(argmin()[0]); } }; using namespace std; // https://atcoder.jp/contests/abc127/tasks/abc127_f namespace ABC127F { signed main() { cin.tie(0); ios::sync_with_stdio(0); int Q; cin >> Q; PiecewiseLinearConvexfunction f; while (Q--) { // debug(Q); int op; cin >> op; if (op == 1) { int a, b; cin >> a >> b; f.add_abs(1, a); f.add_const(b); } else { cout << f.argmin()[0] << " " << f.min() << '\n'; } // f.debugoutput(); } return 0; } } // https://atcoder.jp/contests/kupc2016/tasks/kupc2016_h namespace atcoder_kupc2016_h { signed main() { cin.tie(0); ios::sync_with_stdio(0); int N; cin >> N; long long A[N], B[N]; for (int i= 0; i < N; ++i) cin >> A[i]; for (int i= 0; i < N; ++i) cin >> B[i]; PiecewiseLinearConvexfunction f(1); for (int i= 0; i < N; ++i) { f.cumulative_chmin(); f.shift(B[i] - A[i]); f.add_abs(1, 0); } cout << f.eval(0) << '\n'; return 0; } } // https://yukicoder.me/problems/no/1467 namespace yukicoder1467 { signed main() { cin.tie(0); ios::sync_with_stdio(0); int M, N; cin >> M >> N; long long A[M], B[N]; for (int i= 0; i < M; ++i) cin >> A[i]; for (int j= 0; j < N; ++j) cin >> B[j]; vector vec(A, A + M); for (int j= 0; j < N; ++j) vec.push_back(B[j]); auto id= compress(vec); int n= vec.size(); vector a(n), b(n); for (int i= 0; i < M; ++i) ++a[id(A[i])]; for (int j= 0; j < N; ++j) ++b[id(B[j])]; for (int k= 1; k <= M; ++k) { PiecewiseLinearConvexfunction f(1); for (int i= 0; i < n; ++i) { f.cumulative_chmin(); f.shift(a[i] - b[i] * k); if (i < n - 1) f.add_abs(vec[i + 1] - vec[i], 0); } cout << f.eval(0) << '\n'; } return 0; } } signed main() { cin.tie(0); ios::sync_with_stdio(0); // ABC127F::main(); // atcoder_kupc2016_h::main(); yukicoder1467::main(); return 0; }