struct bounded_flow { int n, m, S, T; dinic net; ll sum; vector fl; vector init; bounded_flow(int n, int m) : sum(0), n(n), m(m), S(0), T(n + 1), net(n + 1), fl(m), init(n + 1) {} void add_edge(int from, int to, ll low, ll high, int edge_id = -1) { if (edge_id != -1) { fl[edge_id] += low; } net.add_edge(from, to, high - low, edge_id, -1); init[to] += low, init[from] -= low; } optional>> run(int s, int t) { for (int i = 1; i <= n; ++i) { if (init[i] > 0) { net.add_edge(S, i, init[i], -1, -1); sum += init[i]; } else if (init[i] < 0) { net.add_edge(i, T, -init[i], -1, -1); } } net.add_edge(t, s, INFLL, -1, -1); if (sum != net.run(S, T)) { return nullopt; } else { auto res_flow = net.run(s, t); for (int from = 1; from <= n; ++from) { for (auto&& [to, cap, flow, rev, mark] : net.edges[from]) { if (mark != -1) { fl[mark] = flow; } } } return {{res_flow, fl}}; } } };