#include using namespace std; // https://judge.yosupo.jp/submission/57330 struct linked_lists { int L, N; vector next, prev; // L: lists are [0...L), N: elements are [0,...N) explicit linked_lists(int L = 0, int N = 0) { assign(L, N); } int rep(int l) const { return l + N; } // "representative" of list l int head(int l) const { return next[rep(l)]; } int tail(int l) const { return prev[rep(l)]; } bool empty(int l) const { return next[rep(l)] == rep(l); } void push_front(int l, int n) { link(rep(l), n, head(l)); } void push_back(int l, int n) { link(tail(l), n, rep(l)); } void insert_before(int i, int n) { link(prev[i], n, i); } void insert_after(int i, int n) { link(i, n, next[i]); } void erase(int n) { link(prev[n], next[n]); } void pop_front(int l) { link(rep(l), next[head(l)]); } void pop_back(int l) { link(prev[tail(l)], rep(l)); } void clear() { iota(begin(next) + N, end(next), N); // sets next[rep(l)] = rep(l) iota(begin(prev) + N, end(prev), N); // sets prev[rep(l)] = rep(l) } void assign(int L, int N) { this->L = L, this->N = N; next.resize(N + L), prev.resize(N + L), clear(); } private: inline void link(int u, int v) { next[u] = v, prev[v] = u; } inline void link(int u, int v, int w) { link(u, v), link(v, w); } }; // Iterate through elements (call them i) of the list #l in "lists" #define FOR_EACH_IN_LINKED_LIST(i, l, lists) \ for (int z##i = l, i = lists.head(z##i); i != lists.rep(z##i); i = lists.next[i]) /** * Network simplex for minimum cost circulation with fixed supply/demand at nodes. * Supports negative costs, negative cost cycles, self-loops and multiple edges fine. * * Flow should be large enough to hold sum of supplies and edge flows * Cost should be large enough to hold sum of absolute costs * 2V (usually >=64 bits) * * Complexity: O(V) expected pivot, O(E) worst-case * * Usage: * network_simplex mcc(V); * for (edges...) { * mcc.add(u, v, cap, cost); * } * for (nodes...) { * mcc.set_supply(u, supply); * mcc.set_demand(u, demand); * } * bool feasible = mcc.mincost_circulation(); * auto mincost = mcc.circulation_cost(); * * References: * LEMON network_simplex.h * OCW MIT MIT15_082JF10_av16.pdf * OCW MIT MIT15_082JF10_lec16.pdf */ template struct network_simplex { // we number the vertices 0,...,V-1, R is given number V. explicit network_simplex(int V) : V(V), node(V + 1) {} void add(int u, int v, Flow cap, Cost cost) { assert(0 <= u && u < V && 0 <= v && v < V); edge.push_back({{u, v}, cap, cost}), E++; } void set_supply(int u, Flow supply) { node[u].supply = supply; } void set_demand(int u, Flow demand) { node[u].supply = -demand; } auto get_supply(int u) const { return node[u].supply; } auto get_potential(int u) const { return node[u].pi; } auto get_flow(int e) const { return edge[e].flow; } auto get_cost(int e) const { return edge[e].cost; } auto reduced_cost(int e) const { auto [u, v] = edge[e].node; return edge[e].cost + node[u].pi - node[v].pi; } template auto circulation_cost() const { CostSum sum = 0; for (int e = 0; e < E; e++) { sum += edge[e].flow * CostSum(edge[e].cost); } return sum; } void verify_spanning_tree() const { for (int e = 0; e < E; e++) { assert(0 <= edge[e].flow && edge[e].flow <= edge[e].cap); assert(edge[e].flow == 0 || reduced_cost(e) <= 0); assert(edge[e].flow == edge[e].cap || reduced_cost(e) >= 0); } } bool mincost_circulation() { static constexpr bool INFEASIBLE = false, OPTIMAL = true; // Check trivialities: positive cap[e] and sum of supplies is 0 Flow sum_supply = 0; for (int u = 0; u < V; u++) { sum_supply += node[u].supply; } if (sum_supply != 0) { return INFEASIBLE; } for (int e = 0; e < E; e++) { if (edge[e].cap < 0) { return INFEASIBLE; } } // Compute inf_cost as sum of all costs + 1, and reset the flow network Cost inf_cost = 1; for (int e = 0; e < E; e++) { edge[e].flow = 0; edge[e].state = STATE_LOWER; inf_cost += abs(edge[e].cost); } edge.resize(E + V); // make space for V artificial edges bfs.resize(V + 1); children.assign(V + 1, V + 1); // Add V artificial edges with infinite cost and initial supply for feasible flow int root = V; node[root] = {-1, -1, 0, 0}; for (int u = 0, e = E; u < V; u++, e++) { // spanning tree links node[u].parent = root, node[u].pred = e; children.push_back(root, u); auto supply = node[u].supply; if (supply >= 0) { node[u].pi = -inf_cost; edge[e] = {{u, root}, supply, inf_cost, supply, STATE_TREE}; } else { node[u].pi = inf_cost; edge[e] = {{root, u}, -supply, inf_cost, -supply, STATE_TREE}; } } // We want to, hopefully, find a pivot edge in O(sqrt(E)). This can be tuned. block_size = max(int(ceil(sqrt(E + V))), min(10, V + 1)); next_arc = 0; // Pivot pivot pivot int in_arc = select_pivot_edge(); while (in_arc != -1) { pivot(in_arc); in_arc = select_pivot_edge(); } // If there is >0 flow through an artificial edge, the problem is infeasible. for (int e = E; e < E + V; e++) { if (edge[e].flow > 0) { edge.resize(E); return INFEASIBLE; } } edge.resize(E); return OPTIMAL; } private: enum ArcState : int8_t { STATE_UPPER = -1, STATE_TREE = 0, STATE_LOWER = 1 }; struct Node { int parent, pred; Flow supply; Cost pi; }; struct Edge { array node; // [0]->[1] Flow cap; Cost cost; Flow flow = 0; ArcState state = STATE_LOWER; }; int V, E = 0, next_arc = 0, block_size = 0; vector node; vector edge; linked_lists children; vector bfs; // scratchpad for downwards bfs and evert int select_pivot_edge() { // block search: check block_size edges looping, and pick the lowest reduced cost Cost minimum = 0; int in_arc = -1; int count = block_size, seen_edges = E + V; for (int& e = next_arc; seen_edges-- > 0; e = e + 1 == E + V ? 0 : e + 1) { if (minimum > edge[e].state * reduced_cost(e)) { minimum = edge[e].state * reduced_cost(e); in_arc = e; } if (--count == 0 && minimum < 0) { break; } else if (count == 0) { count = block_size; } } return in_arc; } void pivot(int in_arc) { // Find lca of u_in and v_in with two pointers technique auto [u_in, v_in] = edge[in_arc].node; int a = u_in, b = v_in; while (a != b) { a = node[a].parent == -1 ? v_in : node[a].parent; b = node[b].parent == -1 ? u_in : node[b].parent; } int lca = a; // Orient the edge so that we add flow along u_in->v_in if (edge[in_arc].state == STATE_UPPER) { swap(u_in, v_in); } // Let's find the saturing flow push enum OutArcSide { SAME_EDGE, U_IN_SIDE, V_IN_SIDE }; OutArcSide side = SAME_EDGE; Flow flow_delta = edge[in_arc].cap; // how much we can push to saturate int u_out = -1; // the exiting arc // Go up from u_in to lca, break ties by prefering lower vertices for (int u = u_in; u != lca && flow_delta > 0; u = node[u].parent) { int e = node[u].pred; bool edge_down = u == edge[e].node[1]; Flow to_saturate = edge_down ? edge[e].cap - edge[e].flow : edge[e].flow; if (flow_delta > to_saturate) { flow_delta = to_saturate; u_out = u; side = U_IN_SIDE; } } // Go up from v_in to lca, break ties by prefering higher vertices for (int u = v_in; u != lca; u = node[u].parent) { int e = node[u].pred; bool edge_up = u == edge[e].node[0]; Flow to_saturate = edge_up ? edge[e].cap - edge[e].flow : edge[e].flow; if (flow_delta >= to_saturate) { flow_delta = to_saturate; u_out = u; side = V_IN_SIDE; } } // Augment along the cycle if we can push anything if (flow_delta > 0) { auto delta = edge[in_arc].state * flow_delta; edge[in_arc].flow += delta; for (int u = edge[in_arc].node[0]; u != lca; u = node[u].parent) { int e = node[u].pred; edge[e].flow += u == edge[e].node[0] ? -delta : delta; } for (int u = edge[in_arc].node[1]; u != lca; u = node[u].parent) { int e = node[u].pred; edge[e].flow += u == edge[e].node[0] ? delta : -delta; } } // Return now if we didn't change the spanning tree. The state of in_arc flipped. if (side == SAME_EDGE) { edge[in_arc].state = ArcState(-edge[in_arc].state); return; } // Basis exchange: Replace out_arc with in_arc in the spanning tree int out_arc = node[u_out].pred; edge[in_arc].state = STATE_TREE; edge[out_arc].state = edge[out_arc].flow ? STATE_UPPER : STATE_LOWER; // Put u_in on the same side as u_out if (side == V_IN_SIDE) { swap(u_in, v_in); } // Evert: Walk up from u_in to u_out, and fix parent/pred/child pointers downwards int i = 0, S = 0; for (int u = u_in; u != u_out; u = node[u].parent) { bfs[S++] = u; } assert(S <= V); for (i = S - 1; i >= 0; i--) { int u = bfs[i], p = node[u].parent; children.erase(p); // remove p from its children list and add it to u's children.push_back(u, p); node[p].parent = u; node[p].pred = node[u].pred; } children.erase(u_in); // remove u_in from its children list and add it to v_in's children.push_back(v_in, u_in); node[u_in].parent = v_in; node[u_in].pred = in_arc; // Fix potentials: Visit the subtree of u_in (pi_delta is not 0). Cost current_pi = reduced_cost(in_arc); Cost pi_delta = u_in == edge[in_arc].node[0] ? -current_pi : current_pi; bfs[0] = u_in; for (i = 0, S = 1; i < S; i++) { int u = bfs[i]; node[u].pi += pi_delta; FOR_EACH_IN_LINKED_LIST (v, u, children) { bfs[S++] = v; } } } }; using ll = long long; int main(){ cin.tie(nullptr); ios::sync_with_stdio(false); ll N, K; cin >> N >> K; network_simplex g(N); g.set_supply(0, K); g.set_demand(N - 1, K); for(ll i = 0; i < N - 1; i++) g.add(i, i + 1, K, 1LL << 30); vector A(N); for(ll i = 0; i < N; i++){ ll M; cin >> A[i] >> M; while(M--){ ll B; cin >> B; B--; if(A[B] < A[i]) g.add(B, i, 1, ((i - B) << 30) - (A[i] - A[B])); } } g.mincost_circulation(); cout << ((K * (N - 1)) << 30) - g.circulation_cost() << endl; }