#line 1 "/home/maspy/compro/library/my_template.hpp" #pragma GCC optimize("Ofast") #pragma GCC optimize("unroll-loops") #include using namespace std; using ll = long long; using pi = pair; using vi = vector; using u32 = unsigned int; using u64 = unsigned long long; using i128 = __int128; template using vc = vector; template using vvc = vector>; template using vvvc = vector>; template using vvvvc = vector>; template using vvvvvc = vector>; template using pq = priority_queue; template using pqg = priority_queue, greater>; #define vec(type, name, ...) vector name(__VA_ARGS__) #define vv(type, name, h, ...) \ vector> name(h, vector(__VA_ARGS__)) #define vvv(type, name, h, w, ...) \ vector>> name( \ h, vector>(w, vector(__VA_ARGS__))) #define vvvv(type, name, a, b, c, ...) \ vector>>> name( \ a, vector>>( \ b, vector>(c, vector(__VA_ARGS__)))) // https://trap.jp/post/1224/ #define FOR1(a) for (ll _ = 0; _ < ll(a); ++_) #define FOR2(i, a) for (ll i = 0; i < ll(a); ++i) #define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i) #define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c)) #define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i) #define FOR4_R(i, a, b, c) for (ll i = (b)-1; i >= ll(a); i -= (c)) #define overload4(a, b, c, d, e, ...) e #define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__) #define FOR_R(...) \ overload4(__VA_ARGS__, FOR4_R, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__) #define FOR_subset(t, s) for (ll t = s; t >= 0; t = (t == 0 ? -1 : (t - 1) & s)) #define all(x) x.begin(), x.end() #define len(x) ll(x.size()) #define elif else if #define eb emplace_back #define mp make_pair #define mt make_tuple #define fi first #define se second #define stoi stoll template T SUM(const vector &A) { T sum = 0; for (auto &&a: A) sum += a; return sum; } #define MIN(v) *min_element(all(v)) #define MAX(v) *max_element(all(v)) #define LB(c, x) distance((c).begin(), lower_bound(all(c), (x))) #define UB(c, x) distance((c).begin(), upper_bound(all(c), (x))) #define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()) int popcnt(int x) { return __builtin_popcount(x); } int popcnt(u32 x) { return __builtin_popcount(x); } int popcnt(ll x) { return __builtin_popcountll(x); } int popcnt(u64 x) { return __builtin_popcountll(x); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2) int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2) int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } template T pick(deque &que) { T a = que.front(); que.pop_front(); return a; } template T pick(pq &que) { T a = que.top(); que.pop(); return a; } template T pick(pqg &que) { assert(que.size()); T a = que.top(); que.pop(); return a; } template T pick(vc &que) { assert(que.size()); T a = que.back(); que.pop_back(); return a; } template T ceil(T x, U y) { return (x > 0 ? (x + y - 1) / y : x / y); } template T floor(T x, U y) { return (x > 0 ? x / y : (x - y + 1) / y); } template pair divmod(T x, U y) { T q = floor(x, y); return {q, x - q * y}; } template ll binary_search(F check, ll ok, ll ng) { assert(check(ok)); while (abs(ok - ng) > 1) { auto x = (ng + ok) / 2; tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x)); } return ok; } template double binary_search_real(F check, double ok, double ng, int iter = 100) { FOR(iter) { double x = (ok + ng) / 2; tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x)); } return (ok + ng) / 2; } template inline bool chmax(T &a, const S &b) { return (a < b ? a = b, 1 : 0); } template inline bool chmin(T &a, const S &b) { return (a > b ? a = b, 1 : 0); } vc s_to_vi(const string &S, char first_char) { vc A(S.size()); FOR(i, S.size()) { A[i] = S[i] - first_char; } return A; } template vector cumsum(vector &A, int off = 1) { int N = A.size(); vector B(N + 1); FOR(i, N) { B[i + 1] = B[i] + A[i]; } if (off == 0) B.erase(B.begin()); return B; } template vc bincount(const vc &A, int size) { vc C(size); for (auto &&x: A) { ++C[x]; } return C; } // stable template vector argsort(const vector &A) { vector ids(A.size()); iota(all(ids), 0); sort(all(ids), [&](int i, int j) { return A[i] < A[j] || (A[i] == A[j] && i < j); }); return ids; } // A[I[0]], A[I[1]], ... template vc rearrange(const vc &A, const vc &I) { int n = len(I); vc B(n); FOR(i, n) B[i] = A[I[i]]; return B; } #line 1 "/home/maspy/compro/library/other/io.hpp" // based on yosupo's fastio #include namespace detail { template std::true_type check_value(int); template std::false_type check_value(long); } // namespace detail template struct is_modint : decltype(detail::check_value(0)) {}; template using is_modint_t = enable_if_t::value>; template using is_not_modint_t = enable_if_t::value>; struct Scanner { FILE *fp; char line[(1 << 15) + 1]; size_t st = 0, ed = 0; void reread() { memmove(line, line + st, ed - st); ed -= st; st = 0; ed += fread(line + ed, 1, (1 << 15) - ed, fp); line[ed] = '\0'; } bool succ() { while (true) { if (st == ed) { reread(); if (st == ed) return false; } while (st != ed && isspace(line[st])) st++; if (st != ed) break; } if (ed - st <= 50) { bool sep = false; for (size_t i = st; i < ed; i++) { if (isspace(line[i])) { sep = true; break; } } if (!sep) reread(); } return true; } template ::value, int> = 0> bool read_single(T &ref) { if (!succ()) return false; while (true) { size_t sz = 0; while (st + sz < ed && !isspace(line[st + sz])) sz++; ref.append(line + st, sz); st += sz; if (!sz || st != ed) break; reread(); } return true; } template ::value, int> = 0> bool read_single(T &ref) { if (!succ()) return false; bool neg = false; if (line[st] == '-') { neg = true; st++; } ref = T(0); while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); } if (neg) ref = -ref; return true; } template * = nullptr> bool read_single(T &ref) { long long val = 0; bool f = read_single(val); ref = T(val); return f; } bool read_single(double &ref) { string s; if (!read_single(s)) return false; ref = std::stod(s); return true; } bool read_single(char &ref) { string s; if (!read_single(s) || s.size() != 1) return false; ref = s[0]; return true; } template bool read_single(vector &ref) { for (auto &d: ref) { if (!read_single(d)) return false; } return true; } template bool read_single(pair &p) { return (read_single(p.first) && read_single(p.second)); } template bool read_single(tuple &p) { return (read_single(get<0>(p)) && read_single(get<1>(p)) && read_single(get<2>(p))); } template bool read_single(tuple &p) { return (read_single(get<0>(p)) && read_single(get<1>(p)) && read_single(get<2>(p)) && read_single(get<3>(p))); } void read() {} template void read(H &h, T &... t) { bool f = read_single(h); assert(f); read(t...); } Scanner(FILE *fp) : fp(fp) {} }; struct Printer { Printer(FILE *_fp) : fp(_fp) {} ~Printer() { flush(); } static constexpr size_t SIZE = 1 << 15; FILE *fp; char line[SIZE], small[50]; size_t pos = 0; void flush() { fwrite(line, 1, pos, fp); pos = 0; } void write(const char &val) { if (pos == SIZE) flush(); line[pos++] = val; } template ::value, int> = 0> void write(T val) { if (pos > (1 << 15) - 50) flush(); if (val == 0) { write('0'); return; } if (val < 0) { write('-'); val = -val; // todo min } size_t len = 0; while (val) { small[len++] = char(0x30 | (val % 10)); val /= 10; } for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; } pos += len; } void write(const string &s) { for (char c: s) write(c); } void write(const char *s) { size_t len = strlen(s); for (size_t i = 0; i < len; i++) write(s[i]); } void write(const double &x) { ostringstream oss; oss << fixed << setprecision(15) << x; string s = oss.str(); write(s); } void write(const long double &x) { ostringstream oss; oss << fixed << setprecision(15) << x; string s = oss.str(); write(s); } template * = nullptr> void write(T &ref) { write(ref.val); } template void write(const vector &val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) write(' '); write(val[i]); } } template void write(const pair &val) { write(val.first); write(' '); write(val.second); } template void write(const tuple &val) { auto &[a, b, c] = val; write(a), write(' '), write(b), write(' '), write(c); } template void write(const tuple &val) { auto &[a, b, c, d] = val; write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d); } template void write(const tuple &val) { auto &[a, b, c, d, e] = val; write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e); } template void write(const tuple &val) { auto &[a, b, c, d, e, f] = val; write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e), write(' '), write(f); } template void write(const array &val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) write(' '); write(val[i]); } } void write(i128 val) { string s; bool negative = 0; if(val < 0){ negative = 1; val = -val; } while (val) { s += '0' + int(val % 10); val /= 10; } if(negative) s += "-"; reverse(all(s)); if (len(s) == 0) s = "0"; write(s); } }; Scanner scanner = Scanner(stdin); Printer printer = Printer(stdout); void flush() { printer.flush(); } void print() { printer.write('\n'); } template void print(Head &&head, Tail &&... tail) { printer.write(head); if (sizeof...(Tail)) printer.write(' '); print(forward(tail)...); } void read() {} template void read(Head &head, Tail &... tail) { scanner.read(head); read(tail...); } #define INT(...) \ int __VA_ARGS__; \ read(__VA_ARGS__) #define LL(...) \ ll __VA_ARGS__; \ read(__VA_ARGS__) #define STR(...) \ string __VA_ARGS__; \ read(__VA_ARGS__) #define CHAR(...) \ char __VA_ARGS__; \ read(__VA_ARGS__) #define DBL(...) \ double __VA_ARGS__; \ read(__VA_ARGS__) #define VEC(type, name, size) \ vector name(size); \ read(name) #define VV(type, name, h, w) \ vector> name(h, vector(w)); \ read(name) void YES(bool t = 1) { print(t ? "YES" : "NO"); } void NO(bool t = 1) { YES(!t); } void Yes(bool t = 1) { print(t ? "Yes" : "No"); } void No(bool t = 1) { Yes(!t); } void yes(bool t = 1) { print(t ? "yes" : "no"); } void no(bool t = 1) { yes(!t); } #line 2 "/home/maspy/compro/library/ds/disjointsparse.hpp" template struct DisjointSparse { using X = typename Monoid::value_type; using value_type = X; int n, log; vc> dat; DisjointSparse() {} DisjointSparse(vc& A) { build(A); } template DisjointSparse(int n, F f) { vc A(n); FOR(i, n) A[i] = f(i); build(A); } void build(vc& A) { n = len(A); log = 1; while ((1 << log) < n) ++log; dat.assign(log, A); FOR(i, log) { auto& v = dat[i]; int b = 1 << i; for (int m = b; m <= n; m += 2 * b) { int L = m - b, R = min(n, m + b); FOR3_R(j, L + 1, m) v[j - 1] = Monoid::op(v[j - 1], v[j]); FOR3(j, m, R - 1) v[j + 1] = Monoid::op(v[j], v[j + 1]); } } } X prod(int L, int R) { if (L == R) return Monoid::unit(); --R; if (L == R) return dat[0][L]; int k = 31 - __builtin_clz(L ^ R); return Monoid::op(dat[k][L], dat[k][R]); } template int max_right(const F& check, int L) { assert(0 <= L && L <= n && check(Monoid::unit())); if (L == n) return n; int ok = L, ng = n + 1; while (ok + 1 < ng) { int k = (ok + ng) / 2; if (check(prod(L, k))) { ok = k; } else { ng = k; } } return ok; } template int min_left(const F& check, int R) { assert(0 <= R && R <= n && check(Monoid::unit())); if (R == 0) return 0; int ok = R, ng = -1; while (ng + 1 < ok) { int k = (ok + ng) / 2; if (check(prod(k, R))) { ok = k; } else { ng = k; } } return ok; } void debug() { print("disjoint sparse table"); FOR(i, log) print(dat[i]); } }; #line 2 "/home/maspy/compro/library/alg/monoid/minmax.hpp" template struct Monoid_MinMax { using P = pair; using value_type = P; static constexpr P op(const P x, const P y) noexcept { return {min(x.fi, y.fi), max(x.se, y.se)}; } static constexpr P from_element(const X x) { return {x, x}; } static constexpr P unit() { return {numeric_limits::max(), numeric_limits::lowest()}; } static constexpr bool commute = true; }; #line 2 "/home/maspy/compro/library/graph/base.hpp" template struct Edge { int frm, to; T cost; int id; }; template struct Graph { int N, M; using cost_type = T; using edge_type = Edge; vector edges; vector indptr; vector csr_edges; vc vc_deg, vc_indeg, vc_outdeg; bool prepared; class OutgoingEdges { public: OutgoingEdges(const Graph* G, int l, int r) : G(G), l(l), r(r) {} const edge_type* begin() const { if (l == r) { return 0; } return &G->csr_edges[l]; } const edge_type* end() const { if (l == r) { return 0; } return &G->csr_edges[r]; } private: const Graph* G; int l, r; }; bool is_prepared() { return prepared; } constexpr bool is_directed() { return directed; } Graph() : N(0), M(0), prepared(0) {} Graph(int N) : N(N), M(0), prepared(0) {} void resize(int n) { N = n; } void add(int frm, int to, T cost = 1, int i = -1) { assert(!prepared); assert(0 <= frm && 0 <= to && to < N); if (i == -1) i = M; auto e = edge_type({frm, to, cost, i}); edges.eb(e); ++M; } // wt, off void read_tree(bool wt = false, int off = 1) { read_graph(N - 1, wt, off); } void read_graph(int M, bool wt = false, int off = 1) { for (int m = 0; m < M; ++m) { INT(a, b); a -= off, b -= off; if (!wt) { add(a, b); } else { T c; read(c); add(a, b, c); } } build(); } void read_parent(int off = 1) { for (int v = 1; v < N; ++v) { INT(p); p -= off; add(p, v); } build(); } void build() { assert(!prepared); prepared = true; indptr.assign(N + 1, 0); for (auto&& e: edges) { indptr[e.frm + 1]++; if (!directed) indptr[e.to + 1]++; } for (int v = 0; v < N; ++v) { indptr[v + 1] += indptr[v]; } auto counter = indptr; csr_edges.resize(indptr.back() + 1); for (auto&& e: edges) { csr_edges[counter[e.frm]++] = e; if (!directed) csr_edges[counter[e.to]++] = edge_type({e.to, e.frm, e.cost, e.id}); } } OutgoingEdges operator[](int v) const { assert(prepared); return {this, indptr[v], indptr[v + 1]}; } vc deg_array() { if (vc_deg.empty()) calc_deg(); return vc_deg; } pair, vc> deg_array_inout() { if (vc_indeg.empty()) calc_deg_inout(); return {vc_indeg, vc_outdeg}; } int deg(int v) { if (vc_deg.empty()) calc_deg(); return vc_deg[v]; } int in_deg(int v) { if (vc_indeg.empty()) calc_deg_inout(); return vc_indeg[v]; } int out_deg(int v) { if (vc_outdeg.empty()) calc_deg_inout(); return vc_outdeg[v]; } void debug() { print("Graph"); if (!prepared) { print("frm to cost id"); for (auto&& e: edges) print(e.frm, e.to, e.cost, e.id); } else { print("indptr", indptr); print("frm to cost id"); FOR(v, N) for (auto&& e: (*this)[v]) print(e.frm, e.to, e.cost, e.id); } } private: void calc_deg() { assert(vc_deg.empty()); vc_deg.resize(N); for (auto&& e: edges) vc_deg[e.frm]++, vc_deg[e.to]++; } void calc_deg_inout() { assert(vc_indeg.empty()); vc_indeg.resize(N); vc_outdeg.resize(N); for (auto&& e: edges) { vc_indeg[e.to]++, vc_outdeg[e.frm]++; } } }; #line 3 "/home/maspy/compro/library/graph/tree.hpp" // HLD euler tour をとっていろいろ。 // 木以外、非連結でも dfs 順序や親がとれる。 template struct TREE { GT &G; using WT = typename GT::cost_type; int N; bool hld; vector LID, RID, head, V, parent, root; vc depth; vc depth_weighted; vector in_tree; TREE(GT &G, int r = -1, bool hld = 1) : G(G), N(G.N), hld(hld), LID(G.N), RID(G.N), head(G.N, r), V(G.N), parent(G.N, -1), root(G.N, -1), depth(G.N, -1), depth_weighted(G.N, 0), in_tree(G.M, 0) { assert(G.is_prepared()); int t1 = 0; if (r != -1) { dfs_sz(r, -1); dfs_hld(r, t1); } else { for (int r = 0; r < N; ++r) { if (parent[r] == -1) { head[r] = r; dfs_sz(r, -1); dfs_hld(r, t1); } } } for (auto &&v: V) root[v] = (parent[v] == -1 ? v : root[parent[v]]); } void dfs_sz(int v, int p) { auto &sz = RID; parent[v] = p; depth[v] = (p == -1 ? 0 : depth[p] + 1); sz[v] = 1; int l = G.indptr[v], r = G.indptr[v + 1]; auto &csr = G.csr_edges; // 使う辺があれば先頭にする for (int i = r - 2; i >= l; --i) { if (hld && depth[csr[i + 1].to] == -1) swap(csr[i], csr[i + 1]); } int hld_sz = 0; for (int i = l; i < r; ++i) { auto e = csr[i]; if (depth[e.to] != -1) continue; in_tree[e.id] = 1; depth_weighted[e.to] = depth_weighted[v] + e.cost; dfs_sz(e.to, v); sz[v] += sz[e.to]; if (hld && chmax(hld_sz, sz[e.to]) && l < i) { swap(csr[l], csr[i]); } } } void dfs_hld(int v, int ×) { LID[v] = times++; RID[v] += LID[v]; V[LID[v]] = v; bool heavy = true; for (auto &&e: G[v]) { if (!in_tree[e.id] || depth[e.to] <= depth[v]) continue; head[e.to] = (heavy ? head[v] : e.to); heavy = false; dfs_hld(e.to, times); } } vc heavy_path_at(int v) { vc P = {v}; while (1) { int a = P.back(); for (auto &&e: G[a]) { if (e.to != parent[a] && head[e.to] == v) { P.eb(e.to); break; } } if (P.back() == a) break; } return P; } int e_to_v(int eid) { auto e = G.edges[eid]; return (parent[e.frm] == e.to ? e.frm : e.to); } int ELID(int v) { return 2 * LID[v] - depth[v]; } int ERID(int v) { return 2 * RID[v] - depth[v] - 1; } /* k: 0-indexed */ int LA(int v, int k) { assert(k <= depth[v]); while (1) { int u = head[v]; if (LID[v] - k >= LID[u]) return V[LID[v] - k]; k -= LID[v] - LID[u] + 1; v = parent[u]; } } int LCA(int u, int v) { for (;; v = parent[head[v]]) { if (LID[u] > LID[v]) swap(u, v); if (head[u] == head[v]) return u; } } int lca(int u, int v) { return LCA(u, v); } int la(int u, int v) { return LA(u, v); } int subtree_size(int v) { return RID[v] - LID[v]; } int dist(int a, int b) { int c = LCA(a, b); return depth[a] + depth[b] - 2 * depth[c]; } WT dist(int a, int b, bool weighted) { assert(weighted); int c = LCA(a, b); return depth_weighted[a] + depth_weighted[b] - WT(2) * depth_weighted[c]; } // a is in b bool in_subtree(int a, int b) { return LID[b] <= LID[a] && LID[a] < RID[b]; } int jump(int a, int b, ll k = 1) { if (k == 1) { if (a == b) return -1; return (in_subtree(b, a) ? LA(b, depth[b] - depth[a] - 1) : parent[a]); } int c = LCA(a, b); int d_ac = depth[a] - depth[c]; int d_bc = depth[b] - depth[c]; if (k > d_ac + d_bc) return -1; if (k <= d_ac) return LA(a, k); return LA(b, d_ac + d_bc - k); } vc collect_child(int v) { vc res; for (auto &&e: G[v]) if (e.to != parent[v]) res.eb(e.to); return res; } vc> get_path_decomposition(int u, int v, bool edge) { // [始点, 終点] の"閉"区間列。 vc> up, down; while (1) { if (head[u] == head[v]) break; if (LID[u] < LID[v]) { down.eb(LID[head[v]], LID[v]); v = parent[head[v]]; } else { up.eb(LID[u], LID[head[u]]); u = parent[head[u]]; } } if (LID[u] < LID[v]) down.eb(LID[u] + edge, LID[v]); elif (LID[v] + edge <= LID[u]) up.eb(LID[u], LID[v] + edge); reverse(all(down)); up.insert(up.end(), all(down)); return up; } void debug() { print("V", V); print("LID", LID); print("RID", RID); print("parent", parent); print("depth", depth); print("head", head); print("in_tree(edge)", in_tree); print("root", root); } }; #line 2 "/home/maspy/compro/library/alg/group/add.hpp" template struct Group_Add { using X = E; using value_type = X; static constexpr X op(const X &x, const X &y) noexcept { return x + y; } static constexpr X inverse(const X &x) noexcept { return -x; } static constexpr X power(const X &x, ll n) noexcept { return X(n) * x; } static constexpr X unit() { return X(0); } static constexpr bool commute = true; }; #line 2 "/home/maspy/compro/library/ds/fenwick2d.hpp" template struct Fenwick2D { using E = typename AbelGroup::value_type; int N; vc keyX; XY min_X; vc indptr; vc keyY; vc dat; Fenwick2D(vc& X, vc& Y, vc& wt) { build(X, Y, wt); } Fenwick2D(vc& X, vc& Y) { vc wt(len(X), AbelGroup::unit()); build(X, Y, wt); } inline int xtoi(XY x) { return (SMALL_X ? clamp(x - min_X, 0, N) : LB(keyX, x)); } inline int nxt(int i) { i += 1; return i + (i & -i) - 1; } inline int prev(int i) { i += 1; return i - (i & -i) - 1; } void build(vc& X, vc& Y, vc& wt) { if (!SMALL_X) { keyX = X; UNIQUE(keyX); N = len(keyX); } else { min_X = (len(X) == 0 ? 0 : MIN(X)); N = (len(X) == 0 ? 0 : MAX(X)) - min_X + 1; keyX.resize(N); FOR(i, N) keyX[i] = min_X + i; } vvc keyY_raw(N); vc> dat_raw(N); auto I = argsort(Y); for (auto&& i: I) { int ix = xtoi(X[i]); ll y = Y[i]; while (ix < N) { auto& KY = keyY_raw[ix]; if (len(KY) == 0 || KY.back() < y) { KY.eb(y); dat_raw[ix].eb(wt[i]); } else { dat_raw[ix].back() = AbelGroup::op(dat_raw[ix].back(), wt[i]); } ix = nxt(ix); } } indptr.assign(N + 1, 0); FOR(i, N) indptr[i + 1] = indptr[i] + len(keyY_raw[i]); keyY.resize(indptr.back()); dat.resize(indptr.back()); FOR(i, N) FOR(j, indptr[i + 1] - indptr[i]) { keyY[indptr[i] + j] = keyY_raw[i][j]; dat[indptr[i] + j] = dat_raw[i][j]; } FOR(i, N) { int n = indptr[i + 1] - indptr[i]; FOR(j, n - 1) { int k = nxt(j); if (k < n) dat[indptr[i] + k] = AbelGroup::op(dat[indptr[i] + k], dat[indptr[i] + j]); } } } void multiply(XY x, XY y, E val) { int i = xtoi(x); assert(keyX[i] == x); while (i < N) { multiply_i(i, y, val); i = nxt(i); } } void add(XY x, XY y, E val) { multiply(x, y, val); } E prod(XY lx, XY ly, XY rx, XY ry) { E pos = AbelGroup::unit(); E neg = AbelGroup::unit(); int L = xtoi(lx) - 1; int R = xtoi(rx) - 1; while (L < R) { pos = AbelGroup::op(pos, prod_i(R, ly, ry)); R = prev(R); } while (R < L) { neg = AbelGroup::op(neg, prod_i(L, ly, ry)); L = prev(L); } E ret = AbelGroup::op(pos, AbelGroup::inverse(neg)); return ret; } E prefix_prod(XY rx, XY ry) { E pos = AbelGroup::unit(); int R = xtoi(rx) - 1; while (R >= 0) { pos = AbelGroup::op(pos, prefix_prod_i(R, ry)); R = prev(R); } return pos; } E sum(XY lx, XY ly, XY rx, XY ry) { return prod(lx, ly, rx, ry); } E prefix_sum(XY rx, XY ry) { return prefix_prod(rx, ry); } void debug() { print("keyX", keyX); print("indptr", indptr); print("keyY", keyY); print("dat", dat); } private: void multiply_i(int i, XY y, E val) { int LID = indptr[i], n = indptr[i + 1] - indptr[i]; auto it = keyY.begin() + LID; int j = lower_bound(it, it + n, y) - it; assert(keyY[LID + j] == y); while (j < n) { dat[LID + j] = AbelGroup::op(dat[LID + j], val); j = nxt(j); } } E prod_i(int i, XY ly, XY ry) { E pos = AbelGroup::unit(); E neg = AbelGroup::unit(); int LID = indptr[i], n = indptr[i + 1] - indptr[i]; auto it = keyY.begin() + LID; int L = lower_bound(it, it + n, ly) - it - 1; int R = lower_bound(it, it + n, ry) - it - 1; while (L < R) { pos = AbelGroup::op(pos, dat[LID + R]); R = prev(R); } while (R < L) { neg = AbelGroup::op(neg, dat[LID + L]); L = prev(L); } return AbelGroup::op(pos, AbelGroup::inverse(neg)); } E prefix_prod_i(int i, XY ry) { E pos = AbelGroup::unit(); int LID = indptr[i], n = indptr[i + 1] - indptr[i]; auto it = keyY.begin() + LID; int R = lower_bound(it, it + n, ry) - it - 1; while (R >= 0) { pos = AbelGroup::op(pos, dat[LID + R]); R = prev(R); } return pos; } }; #line 7 "main.cpp" void solve() { LL(N, K); VEC(int, C, K); for (auto&& x: C) --x; VEC(ll, D, K); Graph G(N); G.read_tree(); TREE tree(G); N = K; const ll INF = 1LL << 60; // suffix のみのとき、および、empty のとき vc SUFF; SUFF.eb(-INF); { int lca = -1; ll sm = 0; FOR_R(i, N) { lca = (lca == -1 ? C[i] : tree.lca(lca, C[i])); sm += D[i]; SUFF.eb(sm + tree.depth[lca]); } } // C[0] との lca の dep vi dep(N); FOR(i, N) dep[i] = tree.depth[tree.lca(C[0], C[i])]; // C[n] までの prefix をとったときの sm と dep vi X1 = D, Y1 = dep; FOR(i, N - 1) X1[i + 1] += X1[i], chmin(Y1[i + 1], Y1[i]); // suffix の個数 -> sm, dep vi X2(N - 1), Y2(N - 1, N); FOR(n, 1, N - 1) { X2[n] = X2[n - 1] + D[N - n]; Y2[n] = min(Y2[n - 1], dep[N - n]); } /* { vi A = SUFF; FOR(a, 0, N - 1) FOR(b, 0, N - 1 - a) { ll x = X1[a] + X2[b] + min(Y1[a], Y2[b]); A.eb(x); } print(A); } */ auto f = [&](ll LIM) -> ll { // LIM 以下となるようなものの数え上げ ll res = 0; for (auto&& x: SUFF) { if (x <= LIM) ++res; } /* FOR(a, N - 1) FOR(b, 0, N - 1 - a) { if (X1[a] + X2[b] + min(Y1[a], Y2[b]) <= LIM) ++res; } */ { /* FOR(a, N - 1) FOR(b, 0, N - 1 - a) { if (Y1[a] < Y2[b] && X1[a] + X2[b] + Y1[a] <= LIM) ++res; } */ Fenwick2D, ll, true> bit(Y2, X2); FOR_R(a, N - 1) { int b = N - 2 - a; bit.add(Y2[b], X2[b], 1); res += bit.sum(Y1[a] + 1, -INF, N + 1, LIM - X1[a] - Y1[a] + 1); } } { /* FOR(a, N - 1) FOR(b, 0, N - 1) { if (b < N - 1 - a && Y1[a] >= Y2[b] && X1[a] + X2[b] + Y2[b] <= LIM) ++res; } */ Fenwick2D, ll, true> bit(Y1, X1); FOR_R(b, N - 1) { int a = N - 2 - b; bit.add(Y1[a], X1[a], 1); res += bit.sum(Y2[b], -INF, N + 1, LIM - X2[b] - Y2[b] + 1); } } return res; }; ll M = N * (N + 1) / 2 + 1; auto check = [&](ll x) -> bool { // med <= x か? ll cnt = f(x); return cnt >= (M - cnt); }; ll ANS = binary_search(check, INF, -INF); print(ANS); } signed main() { cout << fixed << setprecision(15); ll T = 1; // LL(T); FOR(T) solve(); return 0; }