// #define _GLIBCXX_DEBUG #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 &u){if(!u)os<<"0";__int128_t tmp=u<0?(os<<"-",-u):u;std::string s;while(tmp)s+='0'+(tmp%10),tmp/=10;return std::reverse(s.begin(),s.end()),os< 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(); }; } // clang-format off templatestruct make_long{using type= T;}; template<>struct make_long{using type= int16_t;}; template<>struct make_long{using type= uint16_t;}; template<>struct make_long{using type= int32_t;}; template<>struct make_long{using type= uint32_t;}; template<>struct make_long{using type= int64_t;}; template<>struct make_long{using type= uint64_t;}; template<>struct make_long{using type= __int128_t;}; template<>struct make_long{using type= __uint128_t;}; template<>struct make_long{using type= double;}; template<>struct make_long{using type= long double;}; template using make_long_t= typename make_long::type; // clang-format on template class PiecewiseLinearConvex { using D= make_long_t; struct Node { int ch[2], par; T z, x, d, a; D s; size_t sz; friend std::ostream &operator<<(std::ostream &os, const Node &t) { return os << "{z:" << t.z << ",x:" << t.x << ",d:" << t.d << ",a:" << t.a << ",s:" << t.s << ",sz:" << t.sz << ",ch:(" << t.ch[0] << "," << t.ch[1] << "),par:" << t.par << "}"; } }; static inline int ni= 1; static inline Node n[1 << 22]; static inline void info(int t, int d, std::stringstream &ss) { if (!t) return; // push(t); info(n[t].ch[0], d + 1, ss); for (int i= 0; i < d; ++i) ss << " "; ss << " ■ " << n[t] << '\n', info(n[t].ch[1], d + 1, ss); } static inline void dump_xs(int t, std::vector &xs) { if (t) push(t), dump_xs(n[t].ch[0], xs), xs.push_back(n[t].x), dump_xs(n[t].ch[1], xs); } static inline void dump_slopes_l(int t, T ofs, std::vector &as) { if (t) push(t), dump_slopes_l(n[t].ch[1], ofs, as), ofs+= sl(n[t].ch[1]) + n[t].d, as.push_back(-ofs), dump_slopes_l(n[t].ch[0], ofs, as); } static inline void dump_slopes_r(int t, T ofs, std::vector &as) { if (t) push(t), dump_slopes_r(n[t].ch[0], ofs, as), ofs+= sl(n[t].ch[0]) + n[t].d, as.push_back(ofs), dump_slopes_r(n[t].ch[1], ofs, as); } static inline void update(int t) { n[t].sz= 1, n[t].a= n[t].d, n[t].s= D(n[t].x) * n[t].d; if (int l= n[t].ch[0]; l) n[t].sz+= n[l].sz, n[t].a+= n[l].a, n[t].s+= n[l].s; if (int r= n[t].ch[1]; r) n[t].sz+= n[r].sz, n[t].a+= n[r].a, n[t].s+= n[r].s; } static inline void prop(int t, T v) { n[t].z+= v, n[t].s+= D(v) * n[t].a, n[t].x+= v; } static inline void push(int t) { if (n[t].z != 0) { if (n[t].ch[0]) prop(n[t].ch[0], n[t].z); if (n[t].ch[1]) prop(n[t].ch[1], n[t].z); n[t].z= 0; } } static inline void rot(int t) { int p= n[t].par; if (bool d= n[p].ch[1] == t; (n[p].ch[d]= std::exchange(n[t].ch[!d], p))) n[n[p].ch[d]].par= p; if ((n[t].par= std::exchange(n[p].par, t))) n[n[t].par].ch[n[n[t].par].ch[1] == p]= t; update(p); } static inline void splay(int t) { for (int p= n[t].par; p; rot(t), p= n[t].par) if (n[p].par) rot(n[n[p].par].ch[n[p].ch[1] == t] == p ? p : t); } static inline T sl(int t) { return t ? n[t].a : 0; } static inline D sum(int t) { return t ? n[t].s : 0; } template static inline bool lt(T a, T b) { if constexpr (r) return b < a; else return a < b; } template inline D calc_y(int t, T x, T ol, T ou) { if (t) { for (int s;; t= s) { if (push(t); lt(n[t].x, x)) s= n[t].ch[!r]; else { ol+= sl(n[t].ch[!r]), ou+= sum(n[t].ch[!r]); if (n[t].x == x) break; ol+= n[t].d, ou+= D(n[t].x) * n[t].d, s= n[t].ch[r]; } if (!s) break; } splay(t), splay(mn); } if constexpr (r) return D(x) * ol - ou; else return ou - D(x) * ol; } int mn; bool bf[2]; T o[2], rem, bx[2]; D y; D calc_y(T x) { if (!mn) return 0; if (n[mn].x == x) return 0; return x < n[mn].x ? calc_y<0>(n[mn].ch[0], x, o[0], D(n[mn].x) * o[0]) : calc_y<1>(n[mn].ch[1], x, o[1], D(n[mn].x) * o[1]); } void slope_lr(bool r) { int t= mn; if (!t) return; for (; push(t), n[t].ch[r];) t= n[t].ch[r]; D p= sum(n[mn].ch[r]) + D(n[mn].x) * o[r]; T q= o[r] + sl(n[mn].ch[r]); splay(mn= t), o[r]= 0, o[!r]= n[t].d, r ? (y-= p, rem+= q) : (y+= p, rem-= q); } void slope_eval() { if (rem == 0 || !mn) return; bool neg= rem < 0; T p= neg ? -rem : rem, ol= 0; D ou= 0; int t= mn; if (push(t), ol= o[neg]; p <= ol) { o[neg]-= p, o[!neg]+= p, y+= D(n[t].x) * rem, rem= 0; return; } if (ou+= D(n[t].x) * ol, t= n[t].ch[neg]; ol + sl(t) < p) return slope_lr(neg); for (T s, l;;) { if (push(t), s= ol + sl(n[t].ch[!neg]), l= s + n[t].d; p < s) t= n[t].ch[!neg]; else if (l < p) ol= l, ou+= sum(n[t].ch[!neg]) + D(n[t].x) * n[t].d, t= n[t].ch[neg]; else { if (o[neg]= l - p, o[!neg]= p - s; neg) y+= D(n[t].x) * s - (ou + sum(n[t].ch[!neg])); else y-= D(n[t].x) * s - (ou + sum(n[t].ch[!neg])); break; } } splay(mn= t), y+= D(n[t].x) * rem, rem= 0; } template void add_inf(T x0) { if (bf[r] && !lt(bx[r], x0)) return; if (assert(!bf[!r] || !lt(bx[!r], x0)), bf[r]= true, bx[r]= x0; !mn) return; if (slope_lr(!r); !lt(x0, n[mn].x)) return mn= 0, void(); int t= mn, s= t; for (; t;) if (push(t); lt(x0, n[t].x)) s= t, t= n[t].ch[r]; else t= n[t].ch[!r]; splay(s), n[s].ch[r]= 0, splay(mn); } void add_r(int t) { if (t) push(t), add_r(n[t].ch[0]), add_max(0, n[t].d, n[t].x), add_r(n[t].ch[1]); } void add_l(int t) { if (t) push(t), add_l(n[t].ch[0]), add_max(-n[t].d, 0, n[t].x), add_l(n[t].ch[1]); } public: PiecewiseLinearConvex(): mn(0), bf{0, 0}, rem(0), y(0) {} static void clear() { ni= 1; } std::string info() { std::stringstream ss; if (ss << "\n rem:" << rem << ", y:" << y << ", mn:" << mn << "\n bf[0]:" << bf[0] << ", bf[1]:" << bf[1] << ", bx[0]:" << bx[0] << ", bx[1]:" << bx[1] << "\n " << "o[0]:" << o[0] << ", o[1]:" << o[1] << "\n"; mn) info(mn, 0, ss); return ss.str(); } std::vector dump_xs() { std::vector xs; if (bf[0]) xs.push_back(bx[0]); if (mn) dump_xs(mn, xs); if (bf[1]) xs.push_back(bx[1]); return xs; } std::vector> dump_xys() { auto xs= dump_xs(); std::vector> xys(xs.size()); for (int i= xs.size(); i--;) xys[i]= {xs[i], operator()(xs[i])}; return xys; } std::vector dump_slopes() { std::vector as; if (mn) as.push_back(-o[0]), dump_slopes_l(n[mn].ch[0], o[0], as), std::reverse(as.begin(), as.end()), as.push_back(o[1]), dump_slopes_r(n[mn].ch[1], o[1], as); else as.push_back(0); for (auto &a: as) a+= rem; return as; } // f(x) += c void add_const(D c) { y+= c; } // f(x) += ax, / void add_linear(T a) { rem+= a; } // f(x) += max(a(x-x0),b(x-x0)), (a < b) void add_max(T a, T b, T x0) { assert(a < b); if (bf[0] && x0 <= bx[0]) y-= D(b) * x0, rem+= b; else if (bf[1] && bx[1] <= x0) y-= D(a) * x0, rem+= a; else if (mn) { int t= mn; for (;;) { if (push(t); n[t].x == x0) { n[t].d+= b - a; break; } int &s= n[t].ch[n[t].x < x0]; if (!s) { n[s= ni++]= Node{{0, 0}, t, 0, x0, b - a, b - a, D(x0) * (b - a), 1}, t= s; break; } t= s; } if (splay(t), splay(mn); x0 < n[mn].x) y-= D(b) * x0, rem+= b; else if (y-= D(a) * x0, rem+= a; x0 == n[mn].x) o[1]+= b - a; } else n[mn= ni++]= Node{{0, 0}, 0, 0, x0, b - a, b - a, D(x0) * (b - a), 1}, y-= D(a) * x0, rem+= a, o[0]= 0, o[1]= b - a; } // f(x) += max(0, a(x-x0)) void add_ramp(T a, T x0) { if (a != 0) a > 0 ? add_max(0, a, x0) : add_max(a, 0, x0); } // f(x) += a|x-x0|, \/ void add_abs(T a, T x0) { if (assert(a >= 0); a != 0) add_max(-a, a, x0); } // right=false : f(x) += inf (x < x_0), right=true: f(x) += inf (x_0 < x) void add_inf(bool right= false, T x0= 0) { return right ? add_inf<1>(x0) : add_inf<0>(x0); } // f(x) <- f(x-x0) void shift(T x0) { if (bx[0]+= x0, bx[1]+= x0, y-= D(rem) * x0; mn) n[mn].z+= x0, n[mn].x+= x0; } // rev=false: f(x) <- min_{y<=x} f(y), rev=true : f(x) <- min_{x<=y} f(y) void chmin_cum(bool rev= false) { if (bf[0] && bf[1] && bx[0] == bx[1]) y+= D(rem) * bx[0], rem= 0; else if (slope_eval(); rem == 0) { if (mn) n[mn].d= o[rev], o[!rev]= 0, n[mn].ch[!rev]= 0; } else if ((rem > 0) ^ rev) assert(bf[rev]), y+= D(rem) * bx[rev], rem= 0, mn= 0; else if (bf[!rev]) { T p= std::abs(rem); int t= ni++; n[t]= Node{{0, 0}, 0, 0, bx[!rev], p, p, D(bx[!rev]) * p, 1}; if (mn) update(mn), n[t].ch[rev]= mn, n[mn].par= t; mn= t, o[rev]= p, o[!rev]= 0; } bf[!rev]= false; } // f(x) <- min_{lb<=y<=ub} f(x-y). (lb <= ub), \_/ -> \__/ void chmin_slide_win(T lb, T ub) { assert(lb <= ub); if (bf[0] && bf[1] && bx[0] == bx[1]) y+= D(rem) * bx[0], rem= 0; else if (slope_eval(); rem == 0) { if (mn) { if (o[0] == 0) { if (n[mn].z+= ub, n[mn].x+= ub; n[mn].ch[0]) prop(n[mn].ch[0], lb - ub); } else if (o[1] == 0) { if (n[mn].z+= lb, n[mn].x+= lb; n[mn].ch[1]) prop(n[mn].ch[1], ub - lb); } else { int r= n[mn].ch[1], t= ni++; n[t]= Node{{0, r}, mn, 0, n[mn].x, o[1], 0, 0, 1}; if (update(t), prop(n[mn].ch[1]= t, ub - lb), n[mn].d= o[0], o[1]= 0, n[mn].z+= lb, n[mn].x+= lb; r) n[r].par= t; } } } else { bool r= rem > 0; T b[2]= {lb, ub}; if (bf[!r]) { T p= r ? rem : -rem; int t= ni++; n[t]= Node{{0, 0}, 0, 0, bx[!r], p, p, D(bx[!r]) * p, 1}; if (mn) update(mn), n[t].ch[r]= mn, n[mn].par= t; y+= D(rem) * bx[!r], rem= 0, mn= t, n[t].z+= b[r], n[t].x+= b[r], o[r]= p, o[!r]= 0; } else if (y-= D(rem) * b[r]; mn) n[mn].z+= b[r], n[mn].x+= b[r]; } bx[0]+= lb, bx[1]+= ub; } D operator()(T x) { return assert(!bf[0] || bx[0] <= x), assert(!bf[1] || x <= bx[1]), calc_y(x) + D(rem) * x + y; } D min() { return slope_eval(), rem == 0 ? y : rem > 0 ? (assert(bf[0]), y + D(rem) * bx[0]) : (assert(bf[1]), y + D(rem) * bx[1]); } std::array argmin() { slope_eval(); if (rem > 0) { assert(bf[0]); return {bx[0], bx[0]}; } if (rem < 0) { assert(bf[1]); return {bx[1], bx[1]}; } std::array ret= {bx[0], bx[1]}; int t= mn; if (!t) return ret; bool r= o[0] == 0; if (!r && o[1] != 0) ret[0]= ret[1]= n[t].x; else if (ret[r]= n[t].x, t= n[t].ch[!r]; t) { for (; n[t].ch[r];) push(t), t= n[t].ch[r]; splay(t), ret[!r]= n[t].x, splay(mn); } else assert(bf[!r]); return ret; } size_t size() { return mn ? n[mn].sz : 0; } PiecewiseLinearConvex &operator+=(const PiecewiseLinearConvex &r) { if (y+= r.y, rem+= r.rem; r.bf[0]) add_inf(false, r.bx[0]); if (r.bf[1]) add_inf(true, r.bx[1]); if (r.mn) add_l(n[r.mn].ch[0]), add_r(n[r.mn].ch[1]), add_max(-r.o[0], r.o[1], n[r.mn].x); return *this; } }; using namespace std; 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])]; using PLC= PiecewiseLinearConvex; for (int k= 1; k <= M; ++k) { PLC f; f.add_inf(); for (int i= 0; i < n; ++i) { f.chmin_cum(); f.shift(a[i] - b[i] * k); if (i < n - 1) f.add_abs(vec[i + 1] - vec[i], 0); } cout << f(0) << '\n'; PLC::clear(); } return 0; }