// >>> TEMPLATES #include using namespace std; using ll = long long; using ld = long double; using i32 = int32_t; using i64 = int64_t; using u32 = uint32_t; using u64 = uint64_t; #define int ll #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define rep1(i, n) for (int i = 1; i <= (int)(n); i++) #define repR(i, n) for (int i = (int)(n)-1; i >= 0; i--) #define rep1R(i, n) for (int i = (int)(n); i >= 1; i--) #define loop(i, a, B) for (int i = a; i B; i++) #define loopR(i, a, B) for (int i = a; i B; i--) #define all(x) begin(x), end(x) #define allR(x) rbegin(x), rend(x) #define rng(x, l, r) begin(x) + (l), begin(x) + (r) #define pb push_back #define eb emplace_back #define fst first #define snd second template constexpr auto mp(A &&a, B &&b) { return make_pair(forward(a), forward(b)); } template constexpr auto mt(T&&... x) { return make_tuple(forward(x)...); } template auto constexpr inf_ = numeric_limits::max()/2-1; auto constexpr INF32 = inf_; auto constexpr INF64 = inf_; auto constexpr INF = inf_; #ifdef LOCAL #include "debug.hpp" #else #define dump(...) (void)(0) #define say(x) (void)(0) #define debug if (0) #endif template struct pque : priority_queue, Comp> { vector &data() { return this->c; } void clear() { this->c.clear(); } }; template using pque_max = pque>; template using pque_min = pque>; template ::value, int> = 0> ostream& operator<<(ostream& os, T const& a) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; } template ::value, int> = 0> ostream& operator<<(ostream& os, const T (&a)[N]) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; } template ())), class = typename enable_if::value>::type> istream& operator>>(istream& is, T &a) { for (auto& x : a) is >> x; return is; } template ostream& operator<<(ostream& os, pair const& p) { return os << p.first << " " << p.second; } template istream& operator>>(istream& is, pair& p) { return is >> p.first >> p.second; } struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup; template struct FixPoint : private F { constexpr FixPoint(F&& f) : F(forward(f)) {} template constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward(x)...); } }; struct MakeFixPoint { template constexpr auto operator|(F&& f) const { return FixPoint(forward(f)); } }; #define MFP MakeFixPoint()| #define def(name, ...) auto name = MFP [&](auto &&name, __VA_ARGS__) template struct vec_impl { using type = vector::type>; template static type make_v(size_t n, U&&... x) { return type(n, vec_impl::make_v(forward(x)...)); } }; template struct vec_impl { using type = T; static type make_v(T const& x = {}) { return x; } }; template using vec = typename vec_impl::type; template auto make_v(Args&&... args) { return vec_impl::make_v(forward(args)...); } template void quit(T const& x) { cout << x << endl; exit(0); } template constexpr bool chmin(T& x, U const& y) { if (x > (T)y) { x = (T)y; return true; } return false; } template constexpr bool chmax(T& x, U const& y) { if (x < (T)y) { x = (T)y; return true; } return false; } template constexpr auto sumof(It b, It e) { return accumulate(b, e, typename iterator_traits::value_type{}); } template int sz(T const& x) { return x.size(); } template int lbd(C const& v, T const& x) { return lower_bound(begin(v), end(v), x)-begin(v); } template int ubd(C const& v, T const& x) { return upper_bound(begin(v), end(v), x)-begin(v); } constexpr int64_t mod(int64_t x, int64_t m) { assert(m > 0); return (x %= m) < 0 ? x+m : x; } constexpr int64_t div_floor(int64_t x, int64_t y) { assert(y != 0); return x/y - ((x^y) < 0 and x%y); } constexpr int64_t div_ceil(int64_t x, int64_t y) { assert(y != 0); return x/y + ((x^y) > 0 and x%y); } constexpr int dx[] = { 1, 0, -1, 0, 1, -1, -1, 1 }; constexpr int dy[] = { 0, 1, 0, -1, 1, 1, -1, -1 }; constexpr int popcnt(ll x) { return __builtin_popcountll(x); } mt19937_64 seed_{random_device{}()}; template Int rand(Int a, Int b) { return uniform_int_distribution(a, b)(seed_); } i64 irand(i64 a, i64 b) { return rand(a, b); } // [a, b] u64 urand(u64 a, u64 b) { return rand(a, b); } // template void shuffle(It l, It r) { shuffle(l, r, seed_); } template vector &operator--(vector &v) { for (T &x : v) --x; return v; } template vector &operator++(vector &v) { for (T &x : v) ++x; return v; } // <<< // >>> min cost flow template struct MinCostFlow { // Primal-Dual static constexpr Cost inf = numeric_limits::max(); static constexpr Flow EPS = 1e-10; // struct Edge { int32_t to, rev, id; Flow cap; Cost cost; Edge(int to, int rev, int id, Flow cap, Cost cost) : to(to), rev(rev), id(id), cap(cap), cost(cost) {} }; vector> g; vector> es; vector h; // potential vector pv, pe; // previous vertex/edge index int V, E = 0, s = -1, t = -1; Flow next_cap = 0; Cost next_cost = 0; bool neg_edge = false; MinCostFlow(int V = 0) : g(V), h(V), pv(V, -1), pe(V, -1), V(V) {} void add_edge(int from, int to, Flow cap, Cost cost) { assert(from != to); es.emplace_back(from, g[from].size()); g[from].emplace_back(to, g[to].size(), E, cap, cost); g[to].emplace_back(from, g[from].size()-1, E, 0, -cost); E++; if (cost < -EPS) neg_edge = true; } struct edge_t { int32_t from, to; Flow flow, cap; Cost cost; }; Edge& internal_edge(int id) { assert(0 <= id); assert(id < (int)es.size()); int from, idx; tie(from, idx) = es[id]; return g[from][idx]; } edge_t edge(int id) const { assert(0 <= id); assert(id < (int)es.size()); int32_t from, idx; tie(from, idx) = es[id]; auto const& e = g[from][idx]; auto const& r = g[e.to][e.rev]; return { from, e.to, r.cap, e.cap+r.cap, e.cost }; } vector edges() const { vector ret(E); rep (id, E) ret[id] = edge(id); return ret; } template static constexpr bool chmin(T &x, T const& y) { return x > y ? (x = y, true) : false; }; bool BellmanFord(int s) { // use old h say("called"); fill(h.begin(), h.end(), inf); h[s] = 0; bool update = false; rep (_, V-1) { update = false; rep (x, V) if (h[x] < inf) { rep (i, g[x].size()) { auto const& e = g[x][i]; if (e.cap > EPS && chmin(h[e.to], h[x] + e.cost)) { pv[e.to] = x, pe[e.to] = i; update = true; } } } if (not update) break; } assert(not update); // todo: cancel negative loops return true; } void Dijkstra(int s) { // use old h say("called"); using P = pair; priority_queue, greater

> q; vector d(V, inf); d[s] = 0; q.emplace(0, s); while (q.size()) { int val, x; tie(val, x) = q.top(); q.pop(); if (d[x] < val) continue; rep (i, g[x].size()) { auto const& e = g[x][i]; auto cost = e.cost + h[x] - h[e.to]; if (e.cap > EPS && chmin(d[e.to], d[x] + cost)) { pv[e.to] = x, pe[e.to] = i; q.emplace(d[e.to], e.to); } } } rep (x, V) if (d[x] < inf) h[x] += d[x]; else h[x] = inf; } bool dp(int s) { // use old h say("called"); vector top_ord, deg(V); vector> G(V); for (auto [x, i] : es) { int y = g[x][i].to; deg[y]++; G[x].push_back(i); } rep (x, V) if (deg[x] == 0) top_ord.push_back(x); for (int i = 0; i < (int)top_ord.size(); ++i) { int x = top_ord[i]; for (int i : G[x]) { int y = g[x][i].to; if (--deg[y] == 0) top_ord.push_back(y); } } if ((int)top_ord.size() < V) return false; vector d(V, inf); d[s] = 0; for (int x : top_ord) { if (d[x] >= inf-EPS) continue; for (int i : G[x]) { auto const& e = g[x][i]; auto cost = e.cost + h[x] - h[e.to]; if (e.cap > EPS && chmin(d[e.to], d[x] + cost)) { pv[e.to] = x, pe[e.to] = i; } } } rep (x, V) if (d[x] < inf) h[x] += d[x]; else h[x] = inf; return true; } bool calc_next(int s = -1, int t = -1) { if (t < 0) s = this-> s, t = this->t; if (neg_edge) dp(s) or BellmanFord(s), neg_edge = false; else Dijkstra(s); if (h[t] >= inf) { next_cap = 0, next_cost = inf; return false; } next_cap = numeric_limits::max(); for (int x = t; x != s; x = pv[x]) chmin(next_cap, g[pv[x]][pe[x]].cap); next_cost = h[t]; return next_cap > EPS; } void add_flow(Flow flow, int s = -1, int t = -1) { if (t < 0) s = this-> s, t = this->t; for (int x = t; x != s; x = pv[x]) { auto &e = g[pv[x]][pe[x]]; e.cap -= flow; g[x][e.rev].cap += flow; } } pair min_cost_flow(int s, int t, Flow flow) { this->s = s, this->t = t; Cost cost = 0; while (flow > EPS) { if (not calc_next()) return { cost, false }; auto f = min(flow, next_cap); add_flow(f); flow -= f; cost += f * next_cost; } return { cost, true }; } #ifdef LOCAL friend string to_s(MinCostFlow a) { string ret = "\n"; ret += "V = " + to_s(a.V) + ", E = " + to_s(a.E) + "\n"; ret += "s = " + to_s(a.s) + ", t = " + to_s(a.t) + "\n"; for (auto const& p : a.es) { auto const& e = a.g[p.first][p.second]; auto const& r = a.g[e.to][e.rev]; ret += to_s(e.id) + " : "; ret += to_s(p.first) + "->" + to_s(e.to) + ", "; ret += "flow " + to_s(r.cap) + "/" + to_s(e.cap+r.cap) + ", "; ret += "cost " + to_s(e.cost) + "\n"; } return ret; } #endif }; // <<< int32_t main() { int n, k; cin >> n >> k; vector a(n); vector> b(n); rep (i, n) { cin >> a[i]; int m; cin >> m; b[i].resize(m); cin >> b[i]; --b[i]; } MinCostFlow g(n); rep (i, n-1) g.add_edge(i, i+1, INF, 0); rep (i, n) { for (int j : b[i]) { g.add_edge(j, i, 1, a[j] - a[i]); } } auto [cost, ok] = g.min_cost_flow(0, n-1, k); cout << -cost << '\n'; }