// #pragma comment(linker, "/stack:200000000") #include #include #include namespace suisen { // ! utility template using constraints_t = std::enable_if_t, std::nullptr_t>; template constexpr decltype(auto) constexpr_if(Then&& then, OrElse&& or_else) { if constexpr (cond_v) { return std::forward(then); } else { return std::forward(or_else); } } // ! function template using is_same_as_invoke_result = std::is_same, ReturnType>; template using is_uni_op = is_same_as_invoke_result; template using is_bin_op = is_same_as_invoke_result; template using is_comparator = std::is_same, bool>; // ! integral template >> constexpr int bit_num = std::numeric_limits>::digits; template struct is_nbit { static constexpr bool value = bit_num == n; }; template static constexpr bool is_nbit_v = is_nbit::value; // ? template struct safely_multipliable {}; template <> struct safely_multipliable { using type = long long; }; template <> struct safely_multipliable { using type = __int128_t; }; template <> struct safely_multipliable { using type = unsigned long long; }; template <> struct safely_multipliable { using type = __uint128_t; }; template <> struct safely_multipliable { using type = float; }; template <> struct safely_multipliable { using type = double; }; template <> struct safely_multipliable { using type = long double; }; template using safely_multipliable_t = typename safely_multipliable::type; } // namespace suisen // ! type aliases using i128 = __int128_t; using u128 = __uint128_t; using ll = long long; using uint = unsigned int; using ull = unsigned long long; template using vec = std::vector; template using vec2 = vec>; template using vec3 = vec>; template using vec4 = vec>; template using pq_greater = std::priority_queue, std::greater>; template using umap = std::unordered_map; // ! macros (capital: internal macro) #define OVERLOAD2(_1,_2,name,...) name #define OVERLOAD3(_1,_2,_3,name,...) name #define OVERLOAD4(_1,_2,_3,_4,name,...) name #define REP4(i,l,r,s) for(std::remove_reference_t>i=(l);i<(r);i+=(s)) #define REP3(i,l,r) REP4(i,l,r,1) #define REP2(i,n) REP3(i,0,n) #define REPINF3(i,l,s) for(std::remove_reference_t>i=(l);;i+=(s)) #define REPINF2(i,l) REPINF3(i,l,1) #define REPINF1(i) REPINF2(i,0) #define RREP4(i,l,r,s) for(std::remove_reference_t>i=(l)+fld((r)-(l)-1,s)*(s);i>=(l);i-=(s)) #define RREP3(i,l,r) RREP4(i,l,r,1) #define RREP2(i,n) RREP3(i,0,n) #define rep(...) OVERLOAD4(__VA_ARGS__, REP4 , REP3 , REP2 )(__VA_ARGS__) #define rrep(...) OVERLOAD4(__VA_ARGS__, RREP4 , RREP3 , RREP2 )(__VA_ARGS__) #define repinf(...) OVERLOAD3(__VA_ARGS__, REPINF3, REPINF2, REPINF1)(__VA_ARGS__) #define CAT_I(a, b) a##b #define CAT(a, b) CAT_I(a, b) #define UNIQVAR(tag) CAT(tag, __LINE__) #define loop(n) for (std::remove_reference_t> UNIQVAR(loop_variable) = n; UNIQVAR(loop_variable) --> 0;) #define all(iterable) (iterable).begin(), (iterable).end() #define input(type, ...) type __VA_ARGS__; read(__VA_ARGS__) // ! I/O utilities // pair template std::ostream& operator<<(std::ostream& out, const std::pair &a) { return out << a.first << ' ' << a.second; } // tuple template std::ostream& operator<<(std::ostream& out, const std::tuple &a) { if constexpr (N >= std::tuple_size_v>) { return out; } else { out << std::get(a); if constexpr (N + 1 < std::tuple_size_v>) { out << ' '; } return operator<<(out, a); } } // vector template std::ostream& operator<<(std::ostream& out, const std::vector &a) { for (auto it = a.begin(); it != a.end();) { out << *it; if (++it != a.end()) out << ' '; } return out; } // array template std::ostream& operator<<(std::ostream& out, const std::array &a) { for (auto it = a.begin(); it != a.end();) { out << *it; if (++it != a.end()) out << ' '; } return out; } inline void print() { std::cout << '\n'; } template inline void print(const Head &head, const Tail &...tails) { std::cout << head; if (sizeof...(tails)) std::cout << ' '; print(tails...); } template auto print_all(const Iterable& v, std::string sep = " ", std::string end = "\n") -> decltype(std::cout << *v.begin(), void()) { for (auto it = v.begin(); it != v.end();) { std::cout << *it; if (++it != v.end()) std::cout << sep; } std::cout << end; } // pair template std::istream& operator>>(std::istream& in, std::pair &a) { return in >> a.first >> a.second; } // tuple template std::istream& operator>>(std::istream& in, std::tuple &a) { if constexpr (N >= std::tuple_size_v>) { return in; } else { return operator>>(in >> std::get(a), a); } } // vector template std::istream& operator>>(std::istream& in, std::vector &a) { for (auto it = a.begin(); it != a.end(); ++it) in >> *it; return in; } // array template std::istream& operator>>(std::istream& in, std::array &a) { for (auto it = a.begin(); it != a.end(); ++it) in >> *it; return in; } template void read(Args &...args) { ( std::cin >> ... >> args ); } // ! integral utilities // Returns pow(-1, n) template constexpr inline int pow_m1(T n) { return -(n & 1) | 1; } // Returns pow(-1, n) template <> constexpr inline int pow_m1(bool n) { return -int(n) | 1; } // Returns floor(x / y) template constexpr inline T fld(const T x, const T y) { return (x ^ y) >= 0 ? x / y : (x - (y + pow_m1(y >= 0))) / y; } template constexpr inline T cld(const T x, const T y) { return (x ^ y) <= 0 ? x / y : (x + (y + pow_m1(y >= 0))) / y; } template > = nullptr> constexpr inline int popcount(const T x) { return __builtin_popcount(x); } template > = nullptr> constexpr inline int popcount(const T x) { return __builtin_popcount(x); } template > = nullptr> constexpr inline int popcount(const T x) { return __builtin_popcountll(x); } template > = nullptr> constexpr inline int count_lz(const T x) { return x ? __builtin_clz(x) : suisen::bit_num; } template > = nullptr> constexpr inline int count_lz(const T x) { return x ? __builtin_clz(x) : suisen::bit_num; } template > = nullptr> constexpr inline int count_lz(const T x) { return x ? __builtin_clzll(x) : suisen::bit_num; } template > = nullptr> constexpr inline int count_tz(const T x) { return x ? __builtin_ctz(x) : suisen::bit_num; } template > = nullptr> constexpr inline int count_tz(const T x) { return x ? __builtin_ctz(x) : suisen::bit_num; } template > = nullptr> constexpr inline int count_tz(const T x) { return x ? __builtin_ctzll(x) : suisen::bit_num; } template constexpr inline int floor_log2(const T x) { return suisen::bit_num - 1 - count_lz(x); } template constexpr inline int ceil_log2(const T x) { return floor_log2(x) + ((x & -x) != x); } template constexpr inline int kth_bit(const T x, const unsigned int k) { return (x >> k) & 1; } template constexpr inline int parity(const T x) { return popcount(x) & 1; } struct all_subset { struct all_subset_iter { const int s; int t; constexpr all_subset_iter(int s) : s(s), t(s + 1) {} constexpr auto operator*() const { return t; } constexpr auto operator++() {} constexpr auto operator!=(std::nullptr_t) { return t ? (--t &= s, true) : false; } }; int s; constexpr all_subset(int s) : s(s) {} constexpr auto begin() { return all_subset_iter(s); } constexpr auto end() { return nullptr; } }; // ! container template > = nullptr> auto priqueue_comp(const Comparator comparator) { return std::priority_queue, Comparator>(comparator); } template auto isize(const Iterable &iterable) -> decltype(int(iterable.size())) { return iterable.size(); } template > = nullptr> auto generate_vector(int n, Gen generator) { std::vector v(n); for (int i = 0; i < n; ++i) v[i] = generator(i); return v; } template auto generate_range_vector(T l, T r) { return generate_vector(r - l, [l](int i) { return l + i; }); } template auto generate_range_vector(T n) { return generate_range_vector(0, n); } template void sort_unique_erase(std::vector &a) { std::sort(a.begin(), a.end()); a.erase(std::unique(a.begin(), a.end()), a.end()); } template auto foreach_adjacent_values(InputIterator first, InputIterator last, BiConsumer f) -> decltype(f(*first++, *last), void()) { if (first != last) for (auto itr = first, itl = itr++; itr != last; itl = itr++) f(*itl, *itr); } template auto foreach_adjacent_values(Container c, BiConsumer f) -> decltype(c.begin(), c.end(), void()){ foreach_adjacent_values(c.begin(), c.end(), f); } // ! other utilities // x <- min(x, y). returns true iff `x` has chenged. template inline bool chmin(T &x, const T &y) { if (y >= x) return false; x = y; return true; } // x <- max(x, y). returns true iff `x` has chenged. template inline bool chmax(T &x, const T &y) { if (y <= x) return false; x = y; return true; } namespace suisen {} using namespace suisen; using namespace std; struct io_setup { io_setup(int precision = 20) { std::ios::sync_with_stdio(false); std::cin.tie(nullptr); std::cout << std::fixed << std::setprecision(precision); } } io_setup_{}; // ! code from here namespace ei1333 { template< typename T, typename Compare = less< T >, typename RCompare = greater< T > > struct PrioritySumStructure { size_t k; T sum; priority_queue< T, vector< T >, Compare > in, d_in; priority_queue< T, vector< T >, RCompare > out, d_out; PrioritySumStructure(int k) : k(k), sum(0) {} void modify() { while (in.size() - d_in.size() < k && !out.empty()) { auto p = out.top(); out.pop(); if (!d_out.empty() && p == d_out.top()) { d_out.pop(); } else { sum += p; in.emplace(p); } } while (in.size() - d_in.size() > k) { auto p = in.top(); in.pop(); if (!d_in.empty() && p == d_in.top()) { d_in.pop(); } else { sum -= p; out.emplace(p); } } while (!d_in.empty() && in.top() == d_in.top()) { in.pop(); d_in.pop(); } } T query() const { return sum; } void insert(T x) { in.emplace(x); sum += x; modify(); } void erase(T x) { assert(size()); if (!in.empty() && in.top() == x) { sum -= x; in.pop(); } else if (!in.empty() && RCompare()(in.top(), x)) { sum -= x; d_in.emplace(x); } else { d_out.emplace(x); } modify(); } void set_k(size_t kk) { k = kk; modify(); } size_t get_k() const { return k; } size_t size() const { return in.size() + out.size() - d_in.size() - d_out.size(); } }; template< typename T > using MaximumSum = PrioritySumStructure< T, greater< T >, less< T > >; template< typename T > using MinimumSum = PrioritySumStructure< T, less< T >, greater< T > >; } #include #include #include namespace suisen { struct UnionFind { UnionFind() {} explicit UnionFind(int n) : n(n), data(n, -1) {} // Get the root of `x`. equivalent to `operator[](x)` int root(int x) { static std::vector buf; while (data[x] >= 0) buf.push_back(x), x = data[x]; while (buf.size()) data[buf.back()] = x, buf.pop_back(); return x; } // Get the root of `x`. euivalent to `root(x)` int operator[](int x) { return root(x); } // Merge two vertices `x` and `y`. bool merge(int x, int y) { x = root(x), y = root(y); if (x == y) return false; if (data[x] > data[y]) std::swap(x, y); data[x] += data[y], data[y] = x; return true; } // Check if `x` and `y` belongs to the same connected component. bool same(int x, int y) { return root(x) == root(y); } // Get the size of connected componet to which `x` belongs. int size(int x) { return -data[root(x)]; } // Get all of connected components. std::vector> groups() { std::vector> res(n); for (int i = 0; i < n; ++i) res[root(i)].push_back(i); res.erase(std::remove_if(res.begin(), res.end(), [](const auto& g) { return g.empty(); }), res.end()); return res; } private: int n; std::vector data; }; } // namespace suisen namespace suisen { class LinkedUnionFind : public UnionFind { public: LinkedUnionFind() {} explicit LinkedUnionFind(int n) : UnionFind(n), link(n) { std::iota(link.begin(), link.end(), 0); } // Merge two vertices `x` and `y`. bool merge(int x, int y) { if (UnionFind::merge(x, y)) { std::swap(link[x], link[y]); return true; } return false; } // Get items connected to `x` (including `x`). Let the size of return value be `m`, time complexity is O(m). std::vector connected_component(int x) const { std::vector comp {x}; for (int y = link[x]; y != x; y = link[y]) comp.push_back(y); return comp; } private: std::vector link; }; } // namespace suisen int main() { input(int, n, m); vector> edges; rep(i, m) { input(int, u, v); --u, --v; edges.emplace_back(u, v); } vector> c(n); vector s(n); rep(i, n) { read(c[i]); sort(all(c[i]), greater()); s[i] = accumulate(all(c[i]), 0LL); } vector> g(n); rep(i, m) { auto& [u, v] = edges[i]; if (s[u] < s[v]) swap(u, v); g[u].push_back(v); } vector p(n); iota(all(p), 0); sort(all(p), [&](int i, int j) { return s[i] < s[j]; }); auto f = [&](int x) -> bool { // x 1 1 ei1333::MaximumSum cards(3); cards.insert(1), cards.insert(1), cards.insert(x); cards.insert(c[0][0]); // for (long long v : c[0]) cards.insert(v); bool f = true; LinkedUnionFind uf(n); for (int idx = 0; idx < n; ++idx) { int i = p[idx]; if (s[i] >= cards.query()) { return false; } for (int j : g[i]) { assert(s[i] >= s[j]); if (uf.same(i, j)) continue; if (uf.same(0, i)) { for (int k : uf.connected_component(j)) { for (long long v : c[k]) cards.insert(v); } } else if (uf.same(0, j)) { for (int k : uf.connected_component(i)) { for (long long v : c[k]) cards.insert(v); } } uf.merge(i, j); } if (f and uf.size(0) > 1) { cards.insert(c[0][1]); cards.insert(c[0][2]); f = false; } if (uf.same(0, n - 1)) { return true; } } return uf.same(0, n - 1); }; long long l = s[0] - 2, r = 500000000; while (r - l > 1) { long long x = (l + r) >> 1; (f(x) ? r : l) = x; } print(1, 1, r); return 0; }