#include #define overload4(_1, _2, _3, _4, name, ...) name #define rep1(i, n) for (ll i = 0; i < ll(n); ++i) #define rep2(i, s, n) for (ll i = ll(s); i < ll(n); ++i) #define rep3(i, s, n, d) for(ll i = ll(s); i < ll(n); i+=d) #define rep(...) overload4(__VA_ARGS__,rep3,rep2,rep1)(__VA_ARGS__) #define rrep1(i, n) for (ll i = ll(n)-1; i >= 0; i--) #define rrep2(i, n, t) for (ll i = ll(n)-1; i >= (ll)t; i--) #define rrep3(i, n, t, d) for (ll i = ll(n)-1; i >= (ll)t; i-=d) #define rrep(...) overload4(__VA_ARGS__,rrep3,rrep2,rrep1)(__VA_ARGS__) #define all(a) a.begin(),a.end() #define rall(a) a.rbegin(),a.rend() #define SUM(a) accumulate(all(a),0LL) #define MIN(a) *min_element(all(a)) #define MAX(a) *max_element(all(a)) #define SZ(a) int(a.size()) #define popcount(x) __builtin_popcountll(x) #define pf push_front #define pb push_back #define ef emplace_front #define eb emplace_back #define ppf pop_front #define ppb pop_back #ifdef __LOCAL #define debug(...) { cout << #__VA_ARGS__; cout << ": "; print(__VA_ARGS__); cout << flush; } #else #define debug(...) void(0); #endif #define INT(...) int __VA_ARGS__;scan(__VA_ARGS__) #define LL(...) ll __VA_ARGS__;scan(__VA_ARGS__) #define STR(...) string __VA_ARGS__;scan(__VA_ARGS__) #define CHR(...) char __VA_ARGS__;scan(__VA_ARGS__) #define DBL(...) double __VA_ARGS__;scan(__VA_ARGS__) #define LD(...) ld __VA_ARGS__;scan(__VA_ARGS__) using namespace std; using ll = long long; using ld = long double; using P = pair; using LP = pair; using vi = vector; using vvi = vector; using vvvi = vector; using vl = vector; using vvl = vector; using vvvl = vector; using vd = vector; using vvd = vector; using vs = vector; using vc = vector; using vvc = vector; using vb = vector; using vvb = vector; using vp = vector

; using vvp = vector; template istream &operator>>(istream &is, pair &p) { return is >> p.first >> p.second; } template ostream &operator<<(ostream &os, const pair &p) { return os << '{' << p.first << ", " << p.second << '}'; } template istream &operator>>(istream &is, tuple &t) { return is >> get<0>(t) >> get<1>(t) >> get<2>(t); } template ostream &operator<<(ostream &os, const tuple &t) { return os << '{' << get<0>(t) << ", " << get<1>(t) << ", " << get<2>(t) << '}'; } template istream &operator>>(istream &is, vector &v) { for (T &t : v) { is >> t; } return is; } template ostream &operator<<(ostream &os, const vector &v) { os << '['; rep(i, v.size()) os << v[i] << (i == int(v.size() - 1) ? "" : ", "); return os << ']'; } template ostream &operator<<(ostream &os, const set &st) { os << '{'; auto it = st.begin(); while (it != st.end()) { os << (it == st.begin() ? "" : ", ") << *it; it++; } return os << '}'; } template void vecout(const vector &v, char div = '\n') { rep(i, v.size()) cout << v[i] << (i == int(v.size() - 1) ? '\n' : div); } template bool chmin(T &a, T b) { if (a > b) { a = b; return true; } return false; } template bool chmax(T &a, T b) { if (a < b) { a = b; return true; } return false; } void scan() {} template void scan(Head &head, Tail &... tail) { cin >> head; scan(tail...); } template void print(const T &t) { cout << t << '\n'; } template void print(const Head &head, const Tail &... tail) { cout << head << ' '; print(tail...); } template void fin(const T &... a) { print(a...); exit(0); } struct Init_io { Init_io() { ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr); cout << boolalpha << fixed << setprecision(15); cerr << boolalpha << fixed << setprecision(15); } } init_io; const string yes[] = {"no", "yes"}; const string Yes[] = {"No", "Yes"}; const string YES[] = {"NO", "YES"}; const int inf = 1001001001; const ll linf = 1001001001001001001; template vector cumsum(const vector &v, bool shift_one = true) { int n = v.size(); vector res; if (shift_one) { res.resize(n + 1); rep(i, n) res[i + 1] = res[i] + v[i]; } else { res.resize(n); if (n) { res[0] = v[0]; rep(i, 1, n) res[i] = res[i - 1] + v[i]; } } return res; } vvi graph(int n, int m, bool directed = false, int origin = 1) { vvi G(n); rep(_, m) { INT(u, v); u -= origin, v -= origin; G[u].pb(v); if (!directed) G[v].pb(u); } return G; } template vector>> weighted_graph(int n, int m, bool directed = false, int origin = 1) { vector>> G(n); rep(_, m) { int u, v; T w; scan(u, v, w); u -= origin, v -= origin; G[u].eb(v, w); if (!directed) G[v].eb(u, w); } return G; } template class MCF { struct _edge { int to, rev; Cap cap; Cost cost; _edge(int to, int rev, Cap cap, Cost cost) : to(to), rev(rev), cap(cap), cost(cost) {} }; int n; vp pos; vector> G; public: explicit MCF(int n) : n(n), G(n) {} int add_edge(int from, int to, Cap cap, Cost cost) { assert(0 <= from and from < n); assert(0 <= to and to < n); assert(from != to); pos.eb(from, G[from].size()); G[from].eb(to, G[to].size(), cap, cost); G[to].eb(from, G[from].size() - 1, 0, -cost); return pos.size() - 1; } struct edge { int from, to; Cap cap, flow; Cost cost; edge(int from, int to, Cap cap, Cap flow, Cost cost) : from(from), to(to), cap(cap), flow(flow), cost(cost) {} }; edge get_edge(int i) { assert(0 <= i && i < int(pos.size())); auto e = G[pos[i].first][pos[i].second]; auto re = G[e.to][e.rev]; return edge(pos[i].first, e.to, e.cap + re.cap, re.cap, e.cost); } vector edges() { int m = pos.size(); vector res(m); rep(i, m) res[i] = get_edge(i); return res; } pair flow(int s, int t) { return flow(s, t, numeric_limits::max()); } pair flow(int s, int t, Cap flow_limit) { return slope(s, t, flow_limit).back(); } vector> slope(int s, int t) { return slope(s, t, numeric_limits::max()); } // this must not be called more than once // O(F (E + V) log V) vector> slope(int s, int t, Cap flow_limit) { assert(0 <= s and s < n); assert(0 <= t and t < n); assert(s != t); // variants (C = maxcost): // -(n-1)C <= dual[s] <= dual[i] <= dual[t] = 0 // reduced cost (= e.cost + dual[e.from] - dual[e.to]) >= 0 for all _edge vector dual(n, 0), dist(n); vi pv(n), pe(n); vb seen(n); auto dual_ref = [&]() -> bool { fill(all(dist), numeric_limits::max()); fill(all(pv), -1); fill(all(pe), -1); fill(all(seen), false); priority_queue, vector>, greater>> q; dist[s] = 0; q.emplace(0, s); while (not q.empty()) { int u = q.top().second; q.pop(); if (seen[u]) continue; seen[u] = true; if (u == t) break; // dist[u] = shortest(s, u) + dual[s] - dual[u] // dist[u] >= 0 (all reduced cost are positive) // dist[u] <= (n-1)C rep(i, G[u].size()) { auto e = G[u][i]; if (seen[e.to] or !e.cap) continue; // |-dual[e.to] + dual[u]| <= (n-1)C // cost <= C - -(n-1)C + 0 = nC Cost cost = e.cost - dual[e.to] + dual[u]; if (chmin(dist[e.to], dist[u] + cost)) { pv[e.to] = u; pe[e.to] = i; q.emplace(dist[e.to], e.to); } } } if (!seen[t]) { return false; } rep(u, n) { if (!seen[u]) continue; // dual[u] = dual[u] - dist[t] + dist[u] // = dual[u] - (shortest(s, t) + dual[s] - dual[t]) + (shortest(s, u) + dual[s] - dual[u]) // = - shortest(s, t) + dual[t] + shortest(s, v) // = shortest(s, v) - shortest(s, t) >= 0 - (n-1)C dual[u] -= dist[t] - dist[u]; } return true; }; Cap flow = 0; Cost cost = 0, prev_cost_per_flow = -1; vector> res; res.eb(flow, cost); while (flow < flow_limit) { if (!dual_ref()) break; Cap c = flow_limit - flow; for (int u = t; u != s; u = pv[u]) { chmin(c, G[pv[u]][pe[u]].cap); } for (int u = t; u != s; u = pv[u]) { auto &e = G[pv[u]][pe[u]]; e.cap -= c; G[u][e.rev].cap += c; } Cost d = -dual[s]; flow += c; cost += c * d; if (prev_cost_per_flow == d) { res.pop_back(); } res.eb(flow, cost); prev_cost_per_flow = d; } return res; } }; int main() { INT(n, k); vi a(n), m(n); vvi b(n); rep(i, n) { scan(a[i], m[i]); b[i].resize(m[i]); scan(b[i]); for (int &j : b[i]) --j; } MCF mcf(n); ll mx = 1000000000; rep(i, n - 1) mcf.add_edge(i, i + 1, inf, mx); rep(i, n) { for (int j : b[i]) { if (a[j] > a[i]) continue; mcf.add_edge(j, i, 1, mx * (i - j) - (a[i] - a[j])); } } fin(mx * (n - 1) * k - mcf.flow(0, n - 1, k).second); }