#include #include #include #include #include #include #include #include #include namespace atcoder { namespace internal { template struct csr { std::vector start; std::vector elist; csr(int n, const std::vector>& edges) : start(n + 1), elist(edges.size()) { for (auto e : edges) { start[e.first + 1]++; } for (int i = 1; i <= n; i++) { start[i] += start[i - 1]; } auto counter = start; for (auto e : edges) { elist[counter[e.first]++] = e.second; } } }; } // namespace internal } // namespace atcoder #include namespace atcoder { namespace internal { template struct simple_queue { std::vector payload; int pos = 0; void reserve(int n) { payload.reserve(n); } int size() const { return int(payload.size()) - pos; } bool empty() const { return pos == int(payload.size()); } void push(const T& t) { payload.push_back(t); } T& front() { return payload[pos]; } void clear() { payload.clear(); pos = 0; } void pop() { pos++; } }; } // namespace internal } // namespace atcoder namespace atcoder { template struct mcf_graph { public: mcf_graph() {} mcf_graph(int n) : _n(n) {} int add_edge(int from, int to, Cap cap, Cost cost) { assert(0 <= from && from < _n); assert(0 <= to && to < _n); assert(0 <= cap); assert(0 <= cost); int m = int(_edges.size()); _edges.push_back({from, to, cap, 0, cost}); return m; } struct edge { int from, to; Cap cap, flow; Cost cost; }; edge get_edge(int i) { int m = int(_edges.size()); assert(0 <= i && i < m); return _edges[i]; } std::vector edges() { return _edges; } std::pair flow(int s, int t) { return flow(s, t, std::numeric_limits::max()); } std::pair flow(int s, int t, Cap flow_limit) { return slope(s, t, flow_limit).back(); } std::vector> slope(int s, int t) { return slope(s, t, std::numeric_limits::max()); } std::vector> slope(int s, int t, Cap flow_limit) { assert(0 <= s && s < _n); assert(0 <= t && t < _n); assert(s != t); int m = int(_edges.size()); std::vector edge_idx(m); auto g = [&]() { std::vector degree(_n), redge_idx(m); std::vector> elist; elist.reserve(2 * m); for (int i = 0; i < m; i++) { auto e = _edges[i]; edge_idx[i] = degree[e.from]++; redge_idx[i] = degree[e.to]++; elist.push_back({e.from, {e.to, -1, e.cap - e.flow, e.cost}}); elist.push_back({e.to, {e.from, -1, e.flow, -e.cost}}); } auto _g = internal::csr<_edge>(_n, elist); for (int i = 0; i < m; i++) { auto e = _edges[i]; edge_idx[i] += _g.start[e.from]; redge_idx[i] += _g.start[e.to]; _g.elist[edge_idx[i]].rev = redge_idx[i]; _g.elist[redge_idx[i]].rev = edge_idx[i]; } return _g; }(); auto result = slope(g, s, t, flow_limit); for (int i = 0; i < m; i++) { auto e = g.elist[edge_idx[i]]; _edges[i].flow = _edges[i].cap - e.cap; } return result; } private: int _n; std::vector _edges; struct _edge { int to, rev; Cap cap; Cost cost; }; std::vector> slope(internal::csr<_edge>& g, int s, int t, Cap flow_limit) { std::vector> dual_dist(_n); std::vector prev_e(_n); std::vector vis(_n); struct Q { Cost key; int to; bool operator<(Q r) const { return key > r.key; } }; std::vector que_min; std::vector que; auto dual_ref = [&]() { for (int i = 0; i < _n; i++) { dual_dist[i].second = std::numeric_limits::max(); } std::fill(vis.begin(), vis.end(), false); que_min.clear(); que.clear(); size_t heap_r = 0; dual_dist[s].second = 0; que_min.push_back(s); while (!que_min.empty() || !que.empty()) { int v; if (!que_min.empty()) { v = que_min.back(); que_min.pop_back(); } else { while (heap_r < que.size()) { heap_r++; std::push_heap(que.begin(), que.begin() + heap_r); } v = que.front().to; std::pop_heap(que.begin(), que.end()); que.pop_back(); heap_r--; } if (vis[v]) continue; vis[v] = true; if (v == t) break; Cost dual_v = dual_dist[v].first, dist_v = dual_dist[v].second; for (int i = g.start[v]; i < g.start[v + 1]; i++) { auto e = g.elist[i]; if (!e.cap) continue; Cost cost = e.cost - dual_dist[e.to].first + dual_v; if (dual_dist[e.to].second - dist_v > cost) { Cost dist_to = dist_v + cost; dual_dist[e.to].second = dist_to; prev_e[e.to] = e.rev; if (dist_to == dist_v) { que_min.push_back(e.to); } else { que.push_back(Q{dist_to, e.to}); } } } } if (!vis[t]) { return false; } for (int v = 0; v < _n; v++) { if (!vis[v]) continue; dual_dist[v].first -= dual_dist[t].second - dual_dist[v].second; } return true; }; Cap flow = 0; Cost cost = 0, prev_cost_per_flow = -1; std::vector> result = {{Cap(0), Cost(0)}}; while (flow < flow_limit) { if (!dual_ref()) break; Cap c = flow_limit - flow; for (int v = t; v != s; v = g.elist[prev_e[v]].to) { c = std::min(c, g.elist[g.elist[prev_e[v]].rev].cap); } for (int v = t; v != s; v = g.elist[prev_e[v]].to) { auto& e = g.elist[prev_e[v]]; e.cap += c; g.elist[e.rev].cap -= c; } Cost d = -dual_dist[s].first; flow += c; cost += c * d; if (prev_cost_per_flow == d) { result.pop_back(); } result.push_back({flow, cost}); prev_cost_per_flow = d; } return result; } }; } // namespace atcoder using namespace std; using namespace atcoder; #define rep(i,n)for (int i = 0; i < (n); ++i) #define rrep(i,n)for (int i = (n)-1; i >= 0; --i) #define chmax(a, b) a = max(a, b) #define chmin(a, b) a = min(a, b) #define all(x) (x).begin(), (x).end() #define rall(x) (x).rbegin(), (x).rend() using ll = long long; using P = pair; using VI = vector; using VVI = vector; using VL = vector; using VVL = vector; int main() { ios::sync_with_stdio(false); cin.tie(0); int n, k; cin >> n >> k; VI a(n), b(n); rep(i, n) cin >> a[i]; rep(i, n) cin >> b[i]; VVI p(n, VI(n)); rep(i, n) rep(j, n) cin >> p[i][j]; constexpr int pot = 200 * 200; int rnode = n * n, cnode = rnode + n, s = cnode + n, t = s + 1; mcf_graph g(t + 1); rep(i, n) g.add_edge(s, rnode + i, a[i], 0); rep(i, n) rep(j, n) { rep(f, a[i] + 1) { int before = f - p[i][j]; int after = f + 1 - p[i][j]; g.add_edge(rnode + i, i * n + j, 1, pot + after * after - before * before); } g.add_edge(i * n + j, cnode + j, b[j], 0); } rep(j, n) g.add_edge(cnode + j, t, b[j], 0); auto [f, c] = g.flow(s, t); assert(f == k); int ans = c - pot * f; rep(i, n) rep(j, n) ans += p[i][j] * p[i][j]; cout << ans << endl; }