#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 1 "/home/maspy/compro/library/alg/group_xor.hpp" template struct Group_Xor { using value_type = T; using X = value_type; static X op(X x, X y) { return x ^ y; } static constexpr X inverse(const X &x) noexcept { return x; } static constexpr X power(const X &x, ll n) noexcept { return (n & 1 ? x : 0); } static constexpr X unit(){return X(0);}; static constexpr bool commute = true; }; #line 2 "/home/maspy/compro/library/alg/monoid_max.hpp" template struct Monoid_Max { using value_type = X; static constexpr X op(const X &x, const X &y) noexcept { return max(x, y); } static constexpr X unit() { return numeric_limits::lowest(); } static constexpr bool commute = true; }; #line 2 "/home/maspy/compro/library/ds/lazysegtree.hpp" template struct LazySegTree { using Monoid_X = typename Lazy::X_structure; using Monoid_A = typename Lazy::A_structure; using X = typename Monoid_X::value_type; using A = typename Monoid_A::value_type; int n, log, size; vc dat; vc laz; LazySegTree() : LazySegTree(0) {} LazySegTree(int n) : LazySegTree(vc(n, Monoid_X::unit())) {} LazySegTree(vc v) : n(len(v)) { log = 1; while ((1 << log) < n) ++log; size = 1 << log; dat.assign(size << 1, Monoid_X::unit()); laz.assign(size, Monoid_A::unit()); FOR(i, n) dat[size + i] = v[i]; FOR3_R(i, 1, size) update(i); } template LazySegTree(int n, F f) : n(n) { log = 1; while ((1 << log) < n) ++log; size = 1 << log; dat.assign(size << 1, Monoid_X::unit()); laz.assign(size, Monoid_A::unit()); FOR(i, n) dat[size + i] = f(i); FOR3_R(i, 1, size) update(i); } void reset() { fill(all(dat), Monoid_X::unit()); fill(all(laz), Monoid_A::unit()); } void reset(const vc& v) { assert(len(v) == n); reset(); FOR(i, n) dat[size + i] = v[i]; FOR3_R(i, 1, size) update(i); } void update(int k) { dat[k] = Monoid_X::op(dat[2 * k], dat[2 * k + 1]); } void all_apply(int k, A a) { dat[k] = Lazy::act(dat[k], a); if (k < size) laz[k] = Monoid_A::op(laz[k], a); } void push(int k) { all_apply(2 * k, laz[k]); all_apply(2 * k + 1, laz[k]); laz[k] = Monoid_A::unit(); } void set(int p, X x) { assert(0 <= p && p < n); p += size; for (int i = log; i >= 1; i--) push(p >> i); dat[p] = x; for (int i = 1; i <= log; i++) update(p >> i); } X get(int p) { assert(0 <= p && p < n); p += size; for (int i = log; i >= 1; i--) push(p >> i); return dat[p]; } vc get_all() { FOR(i, size) push(i); return {dat.begin() + size, dat.begin() + size + n}; } X prod(int l, int r) { assert(0 <= l && l <= r && r <= n); if (l == r) return Monoid_X::unit(); l += size; r += size; for (int i = log; i >= 1; i--) { if (((l >> i) << i) != l) push(l >> i); if (((r >> i) << i) != r) push((r - 1) >> i); } X xl = Monoid_X::unit(), xr = Monoid_X::unit(); while (l < r) { if (l & 1) xl = Monoid_X::op(xl, dat[l++]); if (r & 1) xr = Monoid_X::op(dat[--r], xr); l >>= 1; r >>= 1; } return Monoid_X::op(xl, xr); } X prod_all() { return dat[1]; } void apply(int p, A a) { assert(0 <= p && p < n); p += size; dat[p] = Lazy::act(dat[p], a); for (int i = 1; i <= log; i++) update(p >> i); } void apply(int l, int r, A a) { assert(0 <= l && l <= r && r <= n); if (l == r) return; l += size; r += size; for (int i = log; i >= 1; i--) { if (((l >> i) << i) != l) push(l >> i); if (((r >> i) << i) != r) push((r - 1) >> i); } { int l2 = l, r2 = r; while (l < r) { if (l & 1) all_apply(l++, a); if (r & 1) all_apply(--r, a); l >>= 1; r >>= 1; } l = l2; r = r2; } for (int i = 1; i <= log; i++) { if (((l >> i) << i) != l) update(l >> i); if (((r >> i) << i) != r) update((r - 1) >> i); } } template int max_right(C& check, int l) { assert(0 <= l && l <= n); assert(check(Monoid_X::unit())); if (l == n) return n; l += size; for (int i = log; i >= 1; i--) push(l >> i); X sm = Monoid_X::unit(); do { while (l % 2 == 0) l >>= 1; if (!check(Monoid_X::op(sm, dat[l]))) { while (l < size) { push(l); l = (2 * l); if (check(Monoid_X::op(sm, dat[l]))) { sm = Monoid_X::op(sm, dat[l]); l++; } } return l - size; } sm = Monoid_X::op(sm, dat[l]); l++; } while ((l & -l) != l); return n; } template int min_left(C& check, int r) { assert(0 <= r && r <= n); assert(check(Monoid_X::unit())); if (r == 0) return 0; r += size; for (int i = log; i >= 1; i--) push((r - 1) >> i); X sm = Monoid_X::unit(); do { r--; while (r > 1 && (r % 2)) r >>= 1; if (!check(Monoid_X::op(dat[r], sm))) { while (r < size) { push(r); r = (2 * r + 1); if (check(Monoid_X::op(dat[r], sm))) { sm = Monoid_X::op(dat[r], sm); r--; } } return r + 1 - size; } sm = Monoid_X::op(dat[r], sm); } while ((r & -r) != r); return 0; } void debug() { print("lazysegtree getall:", get_all()); } }; #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 { Graph &G; using Graph_type = Graph; using WT = typename Graph::cost_type; int N; bool hld; vector LID, RID, head, V, parent, root; vc depth; vc depth_weighted; vector in_tree; TREE(Graph &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 (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); } } 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] - 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/monoid_reverse.hpp" template struct Monoid_Reverse { using value_type = typename Monoid::value_type; using X = value_type; static constexpr X op(const X &x, const X &y) { return Monoid::op(y, x); } static constexpr X unit() { return Monoid::unit(); } static const bool commute = Monoid::commute; }; #line 2 "/home/maspy/compro/library/alg/lazy_reverse.hpp" template struct Lazy_Reverse { using MX = Monoid_Reverse; using MA = typename Lazy::A_structure; using X_structure = MX; using A_structure = MA; using X = typename MX::value_type; using A = typename MA::value_type; static constexpr X act(const X &x, const A &a) { return Lazy::act(x, a); } }; #line 4 "/home/maspy/compro/library/graph/lazytreemonoid.hpp" template struct LazyTreeMonoid { using MonoX = typename Lazy::X_structure; using MonoA = typename Lazy::A_structure; using X = typename MonoX::value_type; using A = typename MonoA::value_type; using RevLazy = Lazy_Reverse; TREE &tree; int N; LazySegTree seg; LazySegTree seg_r; LazyTreeMonoid(TREE &tree) : tree(tree), N(tree.N), seg(tree.N) { if (!MonoX::commute) seg_r = LazySegTree(tree.N); } LazyTreeMonoid(TREE &tree, vc &dat) : tree(tree), N(tree.N) { vc seg_raw(N, MonoX::unit()); if (!edge) { FOR(v, N) seg_raw[tree.LID[v]] = dat[v]; } else { FOR(e, N - 1) { int v = tree.e_to_v(e); seg_raw[tree.LID[v]] = dat[e]; } } seg = LazySegTree(seg_raw); if (!MonoX::commute) seg_r = LazySegTree(seg_raw); } void set(int i, X x) { if (edge) i = tree.e_to_v(i); i = tree.LID[i]; seg.set(i, x); if (!MonoX::commute) seg_r.set(i, x); } X prod_path(int u, int v) { auto pd = tree.get_path_decomposition(u, v, edge); X val = MonoX::unit(); for (auto &&[a, b]: pd) { X x = (a <= b ? seg.prod(a, b + 1) : (MonoX::commute ? seg.prod(b, a + 1) : seg_r.prod(b, a + 1))); val = MonoX::op(val, x); } return val; } X prod_subtree(int u) { int l = tree.LID[u], r = tree.RID[u]; return seg.prod(l + edge, r); } X prod_all() { return seg.prod_all(); } void apply_path(int u, int v, A a) { auto pd = tree.get_path_decomposition(u, v, edge); for (auto &&[x, y]: pd) { int l = min(x, y), r = max(x, y); seg.apply(l, r + 1, a); if (!MonoX::commute) seg_r.apply(l, r + 1, a); } } void apply_subtree(int u, A a) { int l = tree.LID[u], r = tree.RID[u]; return seg.apply(l + edge, r, a); } void debug() { print("tree_monoid"); tree.debug(); seg.debug(); seg_r.debug(); } template int max_path(F &check, int u, int v) { if (edge) return max_path_edge(check, u, v); if (!check(prod_path(u, u))) return -1; auto pd = tree.get_path_decomposition(u, v, edge); X val = MonoX::unit(); for (auto &&[a, b]: pd) { X x = (a <= b ? seg.prod(a, b + 1) : (MonoX::commute ? seg.prod(b, a + 1) : seg_r.prod(b, a + 1))); if (check(MonoX::op(val, x))) { val = MonoX::op(val, x); u = (tree.V[b]); continue; } auto check_tmp = [&](X x) -> bool { return check(MonoX::op(val, x)); }; if (a <= b) { // 下り auto i = seg.max_right(check_tmp, a); return (i == a ? u : tree.V[i - 1]); } else { // 上り auto i = (MonoX::commute ? seg.min_left(check_tmp, a + 1) : seg_r.min_left(check_tmp, a + 1)); if (i == a + 1) return u; return tree.V[i]; } } return v; } private: template int max_path_edge(F &check, int u, int v) { assert(edge); if (!check(MonoX::unit())) return -1; int lca = tree.lca(u, v); auto pd = tree.get_path_decomposition(u, lca, edge); X val = MonoX::unit(); // climb for (auto &&[a, b]: pd) { assert(a >= b); X x = (MonoX::commute ? seg.prod(b, a + 1) : seg_r.prod(b, a + 1)); if (check(MonoX::op(val, x))) { val = MonoX::op(val, x); u = (tree.parent[tree.V[b]]); continue; } auto check_tmp = [&](X x) -> bool { return check(MonoX::op(val, x)); }; auto i = (MonoX::commute ? seg.min_left(check_tmp, a + 1) : seg_r.min_left(check_tmp, a + 1)); if (i == a + 1) return u; return tree.parent[tree.V[i]]; } // down pd = tree.get_path_decomposition(lca, v, edge); for (auto &&[a, b]: pd) { assert(a <= b); X x = seg.prod(a, b + 1); if (check(MonoX::op(val, x))) { val = MonoX::op(val, x); u = (tree.V[b]); continue; } auto check_tmp = [&](X x) -> bool { return check(MonoX::op(val, x)); }; auto i = seg.max_right(check_tmp, a); return (i == a ? u : tree.V[i - 1]); } return v; } }; #line 6 "main.cpp" struct Lazy { using MX = Group_Xor; using MA = Monoid_Max; using X_structure = MX; using A_structure = MA; using X = typename MX::value_type; using A = typename MA::value_type; static constexpr X act(const X &x, const A &a) { if (a == MA::unit()) return x; return 0; } }; void solve() { LL(N); Graph G(N); vc dat; FOR(N - 1) { LL(a, b, x); --a, --b; G.add(a, b); dat.eb(x); } G.build(); TREE tree(G); LazyTreeMonoid X(tree, dat); LL(Q); FOR(Q) { LL(t, x); --x; if (t == 2) { print(X.prod_subtree(x)); } if (t == 1) { X.apply_subtree(x, 0); if (x) X.apply_path(x, tree.parent[x], 0); } } } signed main() { cout << fixed << setprecision(15); ll T = 1; // LL(T); FOR(T) solve(); return 0; }