struct bounded_mcmf {
    int n, m, S, T;
    mcmf net;
    ll sum, pre;
    vector<ll> fl;
    vector<ll> init;
    vector<ll> costs;
    bounded_mcmf(int n, int m) : sum(0), pre(0), n(n), m(m), S(0), T(n + 1), net(n + 1), fl(m), init(n + 1), costs(m) {}
    // handle negative loop case
    void add_edge(int from, int to, ll low, ll high, ll cost, int edge_id = -1) {
        if (cost < 0) {
            __add_edge(from, to, high, high, cost, -1);
            __add_edge(to, from, 0, high - low, -cost, edge_id);
        } else {
            __add_edge(from, to, low, high, cost, edge_id);
        }
        if (edge_id != -1) {
            costs[edge_id] = cost;
            if (cost < 0) {
                fl[edge_id] += high;  // RealFlow = UpperBound - Flow
            } else {
                fl[edge_id] += low;   // RealFlow = LowerBound + Flow
            }
        }
    }
    void __add_edge(int from, int to, ll low, ll high, ll cost, int edge_id = -1) {
        net.add_edge(from, to, high - low, cost, edge_id, -1);
        init[to] += low, init[from] -= low;
        pre += low * cost;
    }
    void prep(int s, int t) {
        for (int i = 1; i <= n; ++i) {
            if (init[i] > 0) {
                net.add_edge(S, i, init[i], 0, -1, -1);
                sum += init[i];
            } else if (init[i] < 0) {
                net.add_edge(i, T, -init[i], 0, -1, -1);
            }
        }
        net.add_edge(t, s, INFLL, 0, -1, -1);
    }
    // min-cost max-flow
    optional<tuple<ll, ll, vector<ll>>> run_mcmf(int s, int t) {  // BUG: unchecked code
        prep(s, t);
        if (sum != net.run(S, T).first) {
            return nullopt;
        } else {
            auto [res_flow, res_cost] = net.run(s, t);
            for (int from = 1; from <= n; ++from) {
                for (auto&& [to, cap, flow, cost, rev, mark] : net.edges[from]) {
                    if (mark != -1) {
                        if (costs[mark] < 0) {
                            fl[mark] -= flow;
                        } else {
                            fl[mark] += flow;
                        }
                    }
                }
            }
            res_cost += pre;
            return {{res_flow, res_cost, fl}};
        }
    }
    // min-cost flow
    optional<tuple<ll, ll, vector<ll>>> run_mcf(int s, int t) {
        prep(s, t);
        auto [res_flow, res_cost] = net.run(S, T);
        res_cost += pre;
        if (sum != res_flow) {
            return nullopt;
        } else {
            for (int from = 1; from <= n; ++from) {
                for (auto&& [to, cap, flow, cost, rev, mark] : net.edges[from]) {
                    if (mark != -1) {
                        if (costs[mark] < 0) {
                            fl[mark] -= flow;
                        } else {
                            fl[mark] += flow;
                        }
                    }
                }
            }
            return {{res_flow, res_cost, fl}};
        }
    }
};