#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } const std::vector> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}}; int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); } template std::pair operator+(const std::pair &l, const std::pair &r) { return std::make_pair(l.first + r.first, l.second + r.second); } template std::pair operator-(const std::pair &l, const std::pair &r) { return std::make_pair(l.first - r.first, l.second - r.second); } template std::vector sort_unique(std::vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template IStream &operator>>(IStream &is, std::vector &vec) { for (auto &v : vec) is >> v; return is; } template OStream &operator<<(OStream &os, const std::vector &vec); template OStream &operator<<(OStream &os, const std::array &arr); template OStream &operator<<(OStream &os, const std::unordered_set &vec); template OStream &operator<<(OStream &os, const pair &pa); template OStream &operator<<(OStream &os, const std::deque &vec); template OStream &operator<<(OStream &os, const std::set &vec); template OStream &operator<<(OStream &os, const std::multiset &vec); template OStream &operator<<(OStream &os, const std::unordered_multiset &vec); template OStream &operator<<(OStream &os, const std::pair &pa); template OStream &operator<<(OStream &os, const std::map &mp); template OStream &operator<<(OStream &os, const std::unordered_map &mp); template OStream &operator<<(OStream &os, const std::tuple &tpl); template OStream &operator<<(OStream &os, const std::vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } template std::istream &operator>>(std::istream &is, std::tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template OStream &operator<<(OStream &os, const std::tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } template OStream &operator<<(OStream &os, const std::unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::pair &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; } template OStream &operator<<(OStream &os, const std::map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl #define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr) #else #define dbg(x) ((void)0) #define dbgif(cond, x) ((void)0) #endif #include int op(int l, int r) { return max(l, r); } int e() { return -(1 << 29); } #include #include #include #include #include #include #include // Heavy-Light Decomposition of trees // Based on http://beet-aizu.hatenablog.com/entry/2017/12/12/235950 struct HeavyLightDecomposition { int V; int k; int nb_heavy_path; std::vector> e; std::vector par; // par[i] = parent of vertex i (Default: -1) std::vector depth; // depth[i] = distance between root and vertex i std::vector subtree_sz; // subtree_sz[i] = size of subtree whose root is i std::vector heavy_child; // heavy_child[i] = child of vertex i on heavy path (Default: -1) std::vector tree_id; // tree_id[i] = id of tree vertex i belongs to std::vector aligned_id, aligned_id_inv; // aligned_id[i] = aligned id for vertex i (consecutive on heavy edges) std::vector head; // head[i] = id of vertex on heavy path of vertex i, nearest to root std::vector head_ids; // consist of head vertex id's std::vector heavy_path_id; // heavy_path_id[i] = heavy_path_id for vertex [i] HeavyLightDecomposition(int sz = 0) : V(sz), k(0), nb_heavy_path(0), e(sz), par(sz), depth(sz), subtree_sz(sz), heavy_child(sz), tree_id(sz, -1), aligned_id(sz), aligned_id_inv(sz), head(sz), heavy_path_id(sz, -1) {} void add_edge(int u, int v) { e[u].emplace_back(v); e[v].emplace_back(u); } void _build_dfs(int root) { std::stack> st; par[root] = -1; depth[root] = 0; st.emplace(root, 0); while (!st.empty()) { int now = st.top().first; int &i = st.top().second; if (i < (int)e[now].size()) { int nxt = e[now][i++]; if (nxt == par[now]) continue; par[nxt] = now; depth[nxt] = depth[now] + 1; st.emplace(nxt, 0); } else { st.pop(); int max_sub_sz = 0; subtree_sz[now] = 1; heavy_child[now] = -1; for (auto nxt : e[now]) { if (nxt == par[now]) continue; subtree_sz[now] += subtree_sz[nxt]; if (max_sub_sz < subtree_sz[nxt]) max_sub_sz = subtree_sz[nxt], heavy_child[now] = nxt; } } } } void _build_bfs(int root, int tree_id_now) { std::queue q({root}); while (!q.empty()) { int h = q.front(); q.pop(); head_ids.emplace_back(h); for (int now = h; now != -1; now = heavy_child[now]) { tree_id[now] = tree_id_now; aligned_id[now] = k++; aligned_id_inv[aligned_id[now]] = now; heavy_path_id[now] = nb_heavy_path; head[now] = h; for (int nxt : e[now]) if (nxt != par[now] and nxt != heavy_child[now]) q.push(nxt); } nb_heavy_path++; } } void build(std::vector roots = {0}) { int tree_id_now = 0; for (auto r : roots) _build_dfs(r), _build_bfs(r, tree_id_now++); } template std::vector segtree_rearrange(const std::vector &data) const { assert(int(data.size()) == V); std::vector ret; ret.reserve(V); for (int i = 0; i < V; i++) ret.emplace_back(data[aligned_id_inv[i]]); return ret; } // query for vertices on path [u, v] (INCLUSIVE) void for_each_vertex(int u, int v, const std::function &f) const { while (true) { if (aligned_id[u] > aligned_id[v]) std::swap(u, v); f(std::max(aligned_id[head[v]], aligned_id[u]), aligned_id[v]); if (head[u] == head[v]) break; v = par[head[v]]; } } void for_each_vertex_noncommutative( int from, int to, const std::function &fup, const std::function &fdown) const { int u = from, v = to; const int lca = lowest_common_ancestor(u, v), dlca = depth[lca]; while (u >= 0 and depth[u] > dlca) { const int p = (depth[head[u]] > dlca ? head[u] : lca); fup(aligned_id[p] + (p == lca), aligned_id[u]), u = par[p]; } static std::vector> lrs; int sz = 0; while (v >= 0 and depth[v] >= dlca) { const int p = (depth[head[v]] >= dlca ? head[v] : lca); if (int(lrs.size()) == sz) lrs.emplace_back(0, 0); lrs.at(sz++) = {p, v}, v = par.at(p); } while (sz--) fdown(aligned_id[lrs.at(sz).first], aligned_id[lrs.at(sz).second]); } // query for edges on path [u, v] void for_each_edge(int u, int v, const std::function &f) const { while (true) { if (aligned_id[u] > aligned_id[v]) std::swap(u, v); if (head[u] != head[v]) { f(aligned_id[head[v]], aligned_id[v]); v = par[head[v]]; } else { if (u != v) f(aligned_id[u] + 1, aligned_id[v]); break; } } } // lowest_common_ancestor: O(log V) int lowest_common_ancestor(int u, int v) const { assert(tree_id[u] == tree_id[v] and tree_id[u] >= 0); while (true) { if (aligned_id[u] > aligned_id[v]) std::swap(u, v); if (head[u] == head[v]) return u; v = par[head[v]]; } } int distance(int u, int v) const { assert(tree_id[u] == tree_id[v] and tree_id[u] >= 0); return depth[u] + depth[v] - 2 * depth[lowest_common_ancestor(u, v)]; } // Level ancestor, O(log V) // if k-th parent is out of range, return -1 int kth_parent(int v, int k) const { if (k < 0) return -1; while (v >= 0) { int h = head.at(v), len = depth.at(v) - depth.at(h); if (k <= len) return aligned_id_inv.at(aligned_id.at(v) - k); k -= len + 1, v = par.at(h); } return -1; } // Jump on tree, O(log V) int s_to_t_by_k_steps(int s, int t, int k) const { if (k < 0) return -1; if (k == 0) return s; int lca = lowest_common_ancestor(s, t); if (k <= depth.at(s) - depth.at(lca)) return kth_parent(s, k); return kth_parent(t, depth.at(s) + depth.at(t) - depth.at(lca) * 2 - k); } }; // UnionFind Tree (0-indexed), based on size of each disjoint set struct UnionFind { std::vector par, cou; UnionFind(int N = 0) : par(N), cou(N, 1) { iota(par.begin(), par.end(), 0); } int find(int x) { return (par[x] == x) ? x : (par[x] = find(par[x])); } bool unite(int x, int y) { x = find(x), y = find(y); if (x == y) return false; if (cou[x] < cou[y]) std::swap(x, y); par[y] = x, cou[x] += cou[y]; return true; } int count(int x) { return cou[find(x)]; } bool same(int x, int y) { return find(x) == find(y); } std::vector> groups() { std::vector> ret(par.size()); for (int i = 0; i < int(par.size()); ++i) ret[find(i)].push_back(i); ret.erase(std::remove_if(ret.begin(), ret.end(), [&](const std::vector &v) { return v.empty(); }), ret.end()); return ret; } }; int main() { int N, K; lint C; cin >> N >> K >> C; vector> wpijs(K); for (auto &[w, p, i, j] : wpijs) { cin >> i >> j >> w >> p; --i, --j; } sort(ALL(wpijs)); dbg(wpijs); UnionFind uf(N); HeavyLightDecomposition hld(N); int ret = 0; lint current_w_sum = 0; vector> used_ijws; for (auto [w, p, i, j] : wpijs) { if (uf.unite(i, j)) { hld.add_edge(i, j); current_w_sum += w; chmax(ret, p); used_ijws.emplace_back(i, j, w); } } if (current_w_sum > C) { puts("-1"); return 0; } hld.build(); vector seginit(N, e()); for (auto [i, j, w] : used_ijws) { if (hld.par.at(i) == j) seginit.at(hld.aligned_id.at(i)) = w; else if (hld.par.at(j) == i) seginit.at(hld.aligned_id.at(j)) = w; else assert(false); } atcoder::segtree seg(seginit); for (auto [w, p, i, j] : wpijs) { if (p <= ret) continue; int tmp = e(); hld.for_each_edge(i, j, [&](int l, int r) { chmax(tmp, seg.prod(l, r + 1)); }); if (current_w_sum - tmp + w <= C) ret = p; } cout << ret << '\n'; }