#include #if __has_include() #include #endif using namespace std; using int64 = long long; const int64 infll = (1LL << 62) - 1; const int inf = (1 << 30) - 1; struct IoSetup { IoSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(10); cerr << fixed << setprecision(10); } } iosetup; template< typename T1, typename T2 > ostream &operator<<(ostream &os, const pair< T1, T2 > &p) { os << p.first << " " << p.second; return os; } template< typename T1, typename T2 > istream &operator>>(istream &is, pair< T1, T2 > &p) { is >> p.first >> p.second; return is; } template< typename T > ostream &operator<<(ostream &os, const vector< T > &v) { for (int i = 0; i < (int) v.size(); i++) { os << v[i] << (i + 1 != v.size() ? " " : ""); } return os; } template< typename T > istream &operator>>(istream &is, vector< T > &v) { for (T &in: v) is >> in; return is; } template< typename T1, typename T2 > inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); } template< typename T1, typename T2 > inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); } template< typename T = int64 > vector< T > make_v(size_t a) { return vector< T >(a); } template< typename T, typename... Ts > auto make_v(size_t a, Ts... ts) { return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...)); } template< typename T, typename V > typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) { t = v; } template< typename T, typename V > typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) { for (auto &e: t) fill_v(e, v); } template< typename F > struct FixPoint: F { explicit FixPoint(F &&f): F(std::forward< F >(f)) {} template< typename... Args > decltype(auto) operator()(Args &&... args) const { return F::operator()(*this, std::forward< Args >(args)...); } }; template< typename F > inline decltype(auto) MFP(F &&f) { return FixPoint< F >{std::forward< F >(f)}; } template< typename Monoid > struct SegmentTree { using S = typename Monoid::S; private: int n, sz; vector< S > seg; Monoid t; public: SegmentTree() = default; explicit SegmentTree(Monoid m, int n): t(m), n(n) { sz = 1; while (sz < n) sz <<= 1; seg.assign(2 * sz, m.e()); } explicit SegmentTree(Monoid m, const vector< S > &v) : SegmentTree(m, (int) v.size()) { build(v); } void build(const vector< S > &v) { assert(n == (int) v.size()); for (int k = 0; k < n; k++) seg[k + sz] = v[k]; for (int k = sz - 1; k > 0; k--) { seg[k] = t.op(seg[2 * k + 0], seg[2 * k + 1]); } } void set(int k, const S &x) { k += sz; seg[k] = x; while (k >>= 1) { seg[k] = t.op(seg[2 * k + 0], seg[2 * k + 1]); } } S get(int k) const { return seg[k + sz]; } S operator[](const int &k) const { return get(k); } void apply(int k, const S &x) { k += sz; seg[k] = t.op(seg[k], x); while (k >>= 1) { seg[k] = t.op(seg[2 * k + 0], seg[2 * k + 1]); } } S prod(int l, int r) const { S L = t.e(), R = t.e(); for (l += sz, r += sz; l < r; l >>= 1, r >>= 1) { if (l & 1) L = t.op(L, seg[l++]); if (r & 1) R = t.op(seg[--r], R); } return t.op(L, R); } S all_prod() const { return seg[1]; } template< typename C > int find_first(int l, const C &check) const { if (l >= n) return n; l += sz; S sum = t.e(); do { while ((l & 1) == 0) l >>= 1; if (check(t.op(sum, seg[l]))) { while (l < sz) { l <<= 1; auto nxt = t.op(sum, seg[l]); if (not check(nxt)) { sum = nxt; l++; } } return l + 1 - sz; } sum = t.op(sum, seg[l++]); } while ((l & -l) != l); return n; } template< typename C > int find_last(int r, const C &check) const { if (r <= 0) return -1; r += sz; S sum = t.e(); do { r--; while (r > 1 and (r & 1)) r >>= 1; if (check(t.op(seg[r], sum))) { while (r < sz) { r = (r << 1) + 1; auto nxt = t.op(seg[r], sum); if (not check(nxt)) { sum = nxt; r--; } } return r - sz; } sum = t.op(seg[r], sum); } while ((r & -r) != r); return -1; } }; template< class T, class OP, class E > struct LambdaMonoid { using S = T; S op(const S &a, const S &b) const { return _op(a, b); } S e() const { return _e(); } LambdaMonoid(OP op, E e): _op(op), _e(e) {} private: OP _op; E _e; }; template< class OP, class E > LambdaMonoid(OP op, E e)->LambdaMonoid< decltype(e()), OP, E >; /* struct Monoid { using S = int; static constexpr S op(const S& a, const S& b) { return a + b; } static constexpr S e() { return 0; } }; */ template struct Edge { int from, to; T cost; int idx; Edge() = default; Edge(int from, int to, T cost = 1, int idx = -1) : from(from), to(to), cost(cost), idx(idx) {} operator int() const { return to; } }; template struct Graph { vector > > g; int es; Graph() = default; explicit Graph(int n) : g(n), es(0) {} size_t size() const { return g.size(); } void add_directed_edge(int from, int to, T cost = 1) { g[from].emplace_back(from, to, cost, es++); } void add_edge(int from, int to, T cost = 1) { g[from].emplace_back(from, to, cost, es); g[to].emplace_back(to, from, cost, es++); } void read(int M, int padding = -1, bool weighted = false, bool directed = false) { for (int i = 0; i < M; i++) { int a, b; cin >> a >> b; a += padding; b += padding; T c = T(1); if (weighted) cin >> c; if (directed) add_directed_edge(a, b, c); else add_edge(a, b, c); } } inline vector > &operator[](const int &k) { return g[k]; } inline const vector > &operator[](const int &k) const { return g[k]; } }; template using Edges = vector >; #line 4 "graph/tree/heavy-light-decomposition.hpp" /** * @brief Heavy-Light-Decomposition(HL分解) * @see https://smijake3.hatenablog.com/entry/2019/09/15/200200 */ template struct HeavyLightDecomposition : Graph { public: using Graph::Graph; using Graph::g; vector sz, in, out, head, rev, par, dep; void build(int root = 0) { sz.assign(g.size(), 0); in.assign(g.size(), 0); out.assign(g.size(), 0); head.assign(g.size(), 0); rev.assign(g.size(), 0); par.assign(g.size(), 0); dep.assign(g.size(), 0); dfs_sz(root, -1, 0); int t = 0; head[root] = root; dfs_hld(root, -1, t); } /* k: 0-indexed */ int la(int v, int k) { while (1) { int u = head[v]; if (in[v] - k >= in[u]) return rev[in[v] - k]; k -= in[v] - in[u] + 1; v = par[u]; } } int lca(int u, int v) const { for (;; v = par[head[v]]) { if (in[u] > in[v]) swap(u, v); if (head[u] == head[v]) return u; } } int dist(int u, int v) const { return dep[u] + dep[v] - 2 * dep[lca(u, v)]; } template E query(int u, int v, const E &ti, const Q &q, const F &f, const S &s, bool edge = false) { E l = ti, r = ti; for (;; v = par[head[v]]) { if (in[u] > in[v]) swap(u, v), swap(l, r); if (head[u] == head[v]) break; l = f(q(in[head[v]], in[v] + 1), l); } return s(f(q(in[u] + edge, in[v] + 1), l), r); } template E query(int u, int v, const E &ti, const Q &q, const F &f, bool edge = false) { return query(u, v, ti, q, f, f, edge); } template void add(int u, int v, const Q &q, bool edge = false) { for (;; v = par[head[v]]) { if (in[u] > in[v]) swap(u, v); if (head[u] == head[v]) break; q(in[head[v]], in[v] + 1); } q(in[u] + edge, in[v] + 1); } /* {parent, child} */ vector > compress(vector &remark) { auto cmp = [&](int a, int b) { return in[a] < in[b]; }; sort(begin(remark), end(remark), cmp); remark.erase(unique(begin(remark), end(remark)), end(remark)); int K = (int)remark.size(); for (int k = 1; k < K; k++) remark.emplace_back(lca(remark[k - 1], remark[k])); sort(begin(remark), end(remark), cmp); remark.erase(unique(begin(remark), end(remark)), end(remark)); vector > es; stack st; for (auto &k : remark) { while (!st.empty() && out[st.top()] <= in[k]) st.pop(); if (!st.empty()) es.emplace_back(st.top(), k); st.emplace(k); } return es; } explicit HeavyLightDecomposition(const Graph &g) : Graph(g) {} private: void dfs_sz(int idx, int p, int d) { dep[idx] = d; par[idx] = p; sz[idx] = 1; if (g[idx].size() && g[idx][0] == p) swap(g[idx][0], g[idx].back()); for (auto &to : g[idx]) { if (to == p) continue; dfs_sz(to, idx, d + 1); sz[idx] += sz[to]; if (sz[g[idx][0]] < sz[to]) swap(g[idx][0], to); } } void dfs_hld(int idx, int p, int ×) { in[idx] = times++; rev[in[idx]] = idx; for (auto &to : g[idx]) { if (to == p) continue; head[to] = (g[idx][0] == to ? head[idx] : to); dfs_hld(to, idx, times); } out[idx] = times; } }; template struct MontgomeryModInt { private: using mint = MontgomeryModInt; using i32 = int32_t; using i64 = int64_t; using u32 = uint32_t; using u64 = uint64_t; static constexpr u32 get_r() { u32 ret = mod_; for (i32 i = 0; i < 4; i++) ret *= 2 - mod_ * ret; return ret; } static constexpr u32 r = get_r(); static constexpr u32 n2 = -u64(mod_) % mod_; static_assert(r * mod_ == 1, "invalid, r * mod != 1"); static_assert(mod_ < (1 << 30), "invalid, mod >= 2 ^ 30"); static_assert((mod_ & 1) == 1, "invalid, mod % 2 == 0"); u32 x; public: MontgomeryModInt() : x{} {} MontgomeryModInt(const i64 &a) : x(reduce(u64(fast ? a : (a % mod() + mod())) * n2)) {} static constexpr u32 reduce(const u64 &b) { return u32(b >> 32) + mod() - u32((u64(u32(b) * r) * mod()) >> 32); } mint &operator+=(const mint &p) { if (i32(x += p.x - 2 * mod()) < 0) x += 2 * mod(); return *this; } mint &operator-=(const mint &p) { if (i32(x -= p.x) < 0) x += 2 * mod(); return *this; } mint &operator*=(const mint &p) { x = reduce(u64(x) * p.x); return *this; } mint &operator/=(const mint &p) { *this *= p.inv(); return *this; } mint operator-() const { return mint() - *this; } mint operator+(const mint &p) const { return mint(*this) += p; } mint operator-(const mint &p) const { return mint(*this) -= p; } mint operator*(const mint &p) const { return mint(*this) *= p; } mint operator/(const mint &p) const { return mint(*this) /= p; } bool operator==(const mint &p) const { return (x >= mod() ? x - mod() : x) == (p.x >= mod() ? p.x - mod() : p.x); } bool operator!=(const mint &p) const { return (x >= mod() ? x - mod() : x) != (p.x >= mod() ? p.x - mod() : p.x); } u32 val() const { u32 ret = reduce(x); return ret >= mod() ? ret - mod() : ret; } mint pow(u64 n) const { mint ret(1), mul(*this); while (n > 0) { if (n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } mint inv() const { return pow(mod() - 2); } friend ostream &operator<<(ostream &os, const mint &p) { return os << p.val(); } friend istream &operator>>(istream &is, mint &a) { i64 t; is >> t; a = mint(t); return is; } static constexpr u32 mod() { return mod_; } }; template using modint = MontgomeryModInt; using modint998244353 = modint<998244353>; using modint1000000007 = modint<1000000007>; template struct SquareMatrix { array, N> A; SquareMatrix() : A{{}} {} size_t size() const { return N; } inline const array &operator[](int k) const { return (A.at(k)); } inline array &operator[](int k) { return (A.at(k)); } static SquareMatrix add_identity() { return SquareMatrix(); } static SquareMatrix mul_identity() { SquareMatrix mat; for (size_t i = 0; i < N; i++) mat[i][i] = 1; return mat; } SquareMatrix &operator+=(const SquareMatrix &B) { for (size_t i = 0; i < N; i++) { for (size_t j = 0; j < N; j++) { (*this)[i][j] += B[i][j]; } } return *this; } SquareMatrix &operator-=(const SquareMatrix &B) { for (size_t i = 0; i < N; i++) { for (size_t j = 0; j < N; j++) { (*this)[i][j] -= B[i][j]; } } return *this; } SquareMatrix &operator*=(const SquareMatrix &B) { array, N> C; for (size_t i = 0; i < N; i++) { for (size_t j = 0; j < N; j++) { for (size_t k = 0; k < N; k++) { C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]); } } } A.swap(C); return (*this); } SquareMatrix &operator^=(uint64_t k) { SquareMatrix B = SquareMatrix::mul_identity(); while (k > 0) { if (k & 1) B *= *this; *this *= *this; k >>= 1LL; } A.swap(B.A); return *this; } SquareMatrix operator+(const SquareMatrix &B) const { return SquareMatrix(*this) += B; } SquareMatrix operator-(const SquareMatrix &B) const { return SquareMatrix(*this) -= B; } SquareMatrix operator*(const SquareMatrix &B) const { return SquareMatrix(*this) *= B; } SquareMatrix operator^(uint64_t k) const { return SquareMatrix(*this) ^= k; } friend ostream &operator<<(ostream &os, SquareMatrix &p) { for (int i = 0; i < N; i++) { os << "["; for (int j = 0; j < N; j++) { os << p[i][j] << (j + 1 == N ? "]\n" : ","); } } return os; } }; using mint = modint1000000007; int main() { int N; cin >> N; vector< int > X(N), Y(N); HeavyLightDecomposition<> g(N); for(int i = 1; i < N; i++) { cin >> X[i] >> Y[i]; g.add_edge(X[i], Y[i]); } g.build(); for(int i = 1; i < N; i++) { if(g.in[X[i]] > g.in[Y[i]]) swap(X[i], Y[i]); } using Mat = SquareMatrix< mint, 2 >; auto f = [](const Mat &a, const Mat &b) { return a * b; }; auto seg = SegmentTree(LambdaMonoid(f, []() { return Mat::mul_identity();}), N); int Q; cin >> Q; while(Q--) { char x; cin >> x; if(x == 'x') { int v; cin >> v; Mat m; cin >> m[0][0] >> m[0][1] >> m[1][0] >> m[1][1]; seg.set(g.in[Y[v + 1]], m); } else { int y, z; cin >> y >> z; auto mat = g.query(y, z, Mat::mul_identity(), [&](int a, int b) { return seg.prod(a, b); }, f, true); cout << mat[0][0] << " " << mat[0][1] << " " << mat[1][0] << " " << mat[1][1] << "\n"; } } }