// #pragma GCC target("avx2") // #pragma GCC optimize("O3") // #pragma GCC optimize("unroll-loops") // #define INTERACTIVE #include using namespace std; namespace templates { // type using ll = long long; using ull = unsigned long long; using Pii = pair; using Pil = pair; using Pli = pair; using Pll = pair; template using pq = priority_queue; template using qp = priority_queue, greater>; // clang-format off #define vec(T, A, ...) vector A(__VA_ARGS__); #define vvec(T, A, h, ...) vector> A(h, vector(__VA_ARGS__)); #define vvvec(T, A, h1, h2, ...) vector>> A(h1, vector>(h2, vector(__VA_ARGS__))); // clang-format on // for loop #define fori1(a) for (ll _ = 0; _ < (a); _++) #define fori2(i, a) for (ll i = 0; i < (a); i++) #define fori3(i, a, b) for (ll i = (a); i < (b); i++) #define fori4(i, a, b, c) for (ll i = (a); ((c) > 0 || i > (b)) && ((c) < 0 || i < (b)); i += (c)) #define overload4(a, b, c, d, e, ...) e #define fori(...) overload4(__VA_ARGS__, fori4, fori3, fori2, fori1)(__VA_ARGS__) // declare and input // clang-format off #define INT(...) int __VA_ARGS__; inp(__VA_ARGS__); #define LL(...) ll __VA_ARGS__; inp(__VA_ARGS__); #define STRING(...) string __VA_ARGS__; inp(__VA_ARGS__); #define CHAR(...) char __VA_ARGS__; inp(__VA_ARGS__); #define DOUBLE(...) double __VA_ARGS__; STRING(str___); __VA_ARGS__ = stod(str___); #define VEC(T, A, n) vector A(n); inp(A); #define VVEC(T, A, n, m) vector> A(n, vector(m)); inp(A); // clang-format on // const value const ll MOD1 = 1000000007; const ll MOD9 = 998244353; const double PI = acos(-1); // other macro #if !defined(RIN__LOCAL) && !defined(INTERACTIVE) #define endl "\n" #endif #define spa ' ' #define len(A) ll(A.size()) #define all(A) begin(A), end(A) // function vector stoc(string &S) { int n = S.size(); vector ret(n); for (int i = 0; i < n; i++) ret[i] = S[i]; return ret; } string ctos(vector &S) { int n = S.size(); string ret = ""; for (int i = 0; i < n; i++) ret += S[i]; return ret; } template auto min(const T &a) { return *min_element(all(a)); } template auto max(const T &a) { return *max_element(all(a)); } template auto clamp(T &a, const S &l, const S &r) { return (a > r ? r : a < l ? l : a); } 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); } template inline bool chclamp(T &a, const S &l, const S &r) { auto b = clamp(a, l, r); return (a != b ? a = b, 1 : 0); } template T sum(vector &A) { T tot = 0; for (auto a : A) tot += a; return tot; } template vector compression(vector X) { sort(all(X)); X.erase(unique(all(X)), X.end()); return X; } // input and output namespace io { // __int128_t std::ostream &operator<<(std::ostream &dest, __int128_t value) { std::ostream::sentry s(dest); if (s) { __uint128_t tmp = value < 0 ? -value : value; char buffer[128]; char *d = std::end(buffer); do { --d; *d = "0123456789"[tmp % 10]; tmp /= 10; } while (tmp != 0); if (value < 0) { --d; *d = '-'; } int len = std::end(buffer) - d; if (dest.rdbuf()->sputn(d, len) != len) { dest.setstate(std::ios_base::badbit); } } return dest; } // vector template istream &operator>>(istream &is, vector &A) { for (auto &a : A) is >> a; return is; } template ostream &operator<<(ostream &os, vector &A) { for (size_t i = 0; i < A.size(); i++) { os << A[i]; if (i != A.size() - 1) os << ' '; } return os; } // vector> template istream &operator>>(istream &is, vector> &A) { for (auto &a : A) is >> a; return is; } template ostream &operator<<(ostream &os, vector> &A) { for (size_t i = 0; i < A.size(); i++) { os << A[i]; if (i != A.size() - 1) os << endl; } return os; } // pair template istream &operator>>(istream &is, pair &A) { is >> A.first >> A.second; return is; } template ostream &operator<<(ostream &os, pair &A) { os << A.first << ' ' << A.second; return os; } // vector> template istream &operator>>(istream &is, vector> &A) { for (size_t i = 0; i < A.size(); i++) { is >> A[i]; } return is; } template ostream &operator<<(ostream &os, vector> &A) { for (size_t i = 0; i < A.size(); i++) { os << A[i]; if (i != A.size() - 1) os << endl; } return os; } // tuple template struct TuplePrint { static ostream &print(ostream &os, const T &t) { TuplePrint::print(os, t); os << ' ' << get(t); return os; } }; template struct TuplePrint { static ostream &print(ostream &os, const T &t) { os << get<0>(t); return os; } }; template ostream &operator<<(ostream &os, const tuple &t) { TuplePrint::print(os, t); return os; } // io functions void FLUSH() { cout << flush; } void print() { cout << endl; } template void print(Head &&head, Tail &&...tail) { cout << head; if (sizeof...(Tail)) cout << spa; print(std::forward(tail)...); } template void prisep(vector &A, S sep) { int n = A.size(); for (int i = 0; i < n; i++) { cout << A[i]; if (i != n - 1) cout << sep; } cout << endl; } template void priend(T A, S end) { cout << A << end; } template void prispa(T A) { priend(A, spa); } template bool printif(bool f, T A, S B) { if (f) print(A); else print(B); return f; } template void inp(T &...a) { (cin >> ... >> a); } } // namespace io using namespace io; // read graph vector> read_edges(int n, int m, bool direct = false, int indexed = 1) { vector> edges(n, vector()); for (int i = 0; i < m; i++) { INT(u, v); u -= indexed; v -= indexed; edges[u].push_back(v); if (!direct) edges[v].push_back(u); } return edges; } vector> read_tree(int n, int indexed = 1) { return read_edges(n, n - 1, false, indexed); } template vector>> read_wedges(int n, int m, bool direct = false, int indexed = 1) { vector>> edges(n, vector>()); for (int i = 0; i < m; i++) { INT(u, v); T w; inp(w); u -= indexed; v -= indexed; edges[u].push_back({v, w}); if (!direct) edges[v].push_back({u, w}); } return edges; } template vector>> read_wtree(int n, int indexed = 1) { return read_wedges(n, n - 1, false, indexed); } // yes / no namespace yesno { // yes inline bool yes(bool f = true) { cout << (f ? "yes" : "no") << endl; return f; } inline bool Yes(bool f = true) { cout << (f ? "Yes" : "No") << endl; return f; } inline bool YES(bool f = true) { cout << (f ? "YES" : "NO") << endl; return f; } // no inline bool no(bool f = true) { cout << (!f ? "yes" : "no") << endl; return f; } inline bool No(bool f = true) { cout << (!f ? "Yes" : "No") << endl; return f; } inline bool NO(bool f = true) { cout << (!f ? "YES" : "NO") << endl; return f; } // possible inline bool possible(bool f = true) { cout << (f ? "possible" : "impossible") << endl; return f; } inline bool Possible(bool f = true) { cout << (f ? "Possible" : "Impossible") << endl; return f; } inline bool POSSIBLE(bool f = true) { cout << (f ? "POSSIBLE" : "IMPOSSIBLE") << endl; return f; } // impossible inline bool impossible(bool f = true) { cout << (!f ? "possible" : "impossible") << endl; return f; } inline bool Impossible(bool f = true) { cout << (!f ? "Possible" : "Impossible") << endl; return f; } inline bool IMPOSSIBLE(bool f = true) { cout << (!f ? "POSSIBLE" : "IMPOSSIBLE") << endl; return f; } // Alice Bob inline bool Alice(bool f = true) { cout << (f ? "Alice" : "Bob") << endl; return f; } inline bool Bob(bool f = true) { cout << (f ? "Bob" : "Alice") << endl; return f; } // Takahashi Aoki inline bool Takahashi(bool f = true) { cout << (f ? "Takahashi" : "Aoki") << endl; return f; } inline bool Aoki(bool f = true) { cout << (f ? "Aoki" : "Takahashi") << endl; return f; } } // namespace yesno using namespace yesno; } // namespace templates using namespace templates; template struct segtree { public: segtree() : segtree(0) {} explicit segtree(int n) : segtree(std::vector(n, e())) {}; explicit segtree(const std::vector &v) : _n(int(v.size())) { size = 1; log = 0; while (size < _n) { log++; size <<= 1; } d = std::vector(2 * size, e()); for (int i = 0; i < _n; i++) d[size + i] = v[i]; for (int i = size - 1; i >= 1; i--) update(i); } void set(int p, S x) { assert(0 <= p && p < _n); p += size; d[p] = x; for (int i = 1; i <= log; i++) update(p >> i); } S get(int p) { assert(0 <= p && p < _n); return d[p + size]; } S prod(int l, int r) { assert(0 <= l && l <= r && r <= _n); S sml = e(), smr = e(); l += size; r += size; while (l < r) { if (l & 1) sml = op(sml, d[l++]); if (r & 1) smr = op(d[--r], smr); l >>= 1; r >>= 1; } return op(sml, smr); } private: int _n, size, log; std::vector d; void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); } }; template struct Modint { int x; Modint() : x(0) {} Modint(int64_t y) { if (y >= 0) x = y % MOD; else x = (y % MOD + MOD) % MOD; } Modint &operator+=(const Modint &p) { x += p.x; if (x >= MOD) x -= MOD; return *this; } Modint &operator-=(const Modint &p) { x -= p.x; if (x < 0) x += MOD; return *this; } Modint &operator*=(const Modint &p) { x = int(1LL * x * p.x % MOD); return *this; } Modint &operator/=(const Modint &p) { *this *= p.inverse(); return *this; } Modint &operator%=(const Modint &p) { assert(p.x == 0); return *this; } Modint operator-() const { return Modint(-x); } Modint &operator++() { x++; if (x == MOD) x = 0; return *this; } Modint &operator--() { if (x == 0) x = MOD; x--; return *this; } Modint operator++(int) { Modint result = *this; ++*this; return result; } Modint operator--(int) { Modint result = *this; --*this; return result; } friend Modint operator+(const Modint &lhs, const Modint &rhs) { return Modint(lhs) += rhs; } friend Modint operator-(const Modint &lhs, const Modint &rhs) { return Modint(lhs) -= rhs; } friend Modint operator*(const Modint &lhs, const Modint &rhs) { return Modint(lhs) *= rhs; } friend Modint operator/(const Modint &lhs, const Modint &rhs) { return Modint(lhs) /= rhs; } friend Modint operator%(const Modint &lhs, const Modint &rhs) { assert(rhs.x == 0); return Modint(lhs); } bool operator==(const Modint &p) const { return x == p.x; } bool operator!=(const Modint &p) const { return x != p.x; } bool operator<(const Modint &rhs) const { return x < rhs.x; } bool operator<=(const Modint &rhs) const { return x <= rhs.x; } bool operator>(const Modint &rhs) const { return x > rhs.x; } bool operator>=(const Modint &rhs) const { return x >= rhs.x; } Modint inverse() const { int a = x, b = MOD, u = 1, v = 0, t; while (b > 0) { t = a / b; a -= t * b; u -= t * v; std::swap(a, b); std::swap(u, v); } return Modint(u); } Modint pow(int64_t k) const { Modint ret(1); Modint y(x); while (k > 0) { if (k & 1) ret *= y; y *= y; k >>= 1; } return ret; } std::pair to_frac(int max_n = 1000) const { int y = x; for (int i = 1; i <= max_n; i++) { if (y <= max_n) { return {y, i}; } else if (MOD - y <= max_n) { return {-(MOD - y), i}; } y = (y + x) % MOD; } return {-1, -1}; } friend std::ostream &operator<<(std::ostream &os, const Modint &p) { return os << p.x; } friend std::istream &operator>>(std::istream &is, Modint &p) { int64_t y; is >> y; p = Modint(y); return (is); } static int get_mod() { return MOD; } }; struct Arbitrary_Modint { int x; static int MOD; static void set_mod(int mod) { MOD = mod; } Arbitrary_Modint() : x(0) {} Arbitrary_Modint(int64_t y) { if (y >= 0) x = y % MOD; else x = (y % MOD + MOD) % MOD; } Arbitrary_Modint &operator+=(const Arbitrary_Modint &p) { x += p.x; if (x >= MOD) x -= MOD; return *this; } Arbitrary_Modint &operator-=(const Arbitrary_Modint &p) { x -= p.x; if (x < 0) x += MOD; return *this; } Arbitrary_Modint &operator*=(const Arbitrary_Modint &p) { x = int(1LL * x * p.x % MOD); return *this; } Arbitrary_Modint &operator/=(const Arbitrary_Modint &p) { *this *= p.inverse(); return *this; } Arbitrary_Modint &operator%=(const Arbitrary_Modint &p) { assert(p.x == 0); return *this; } Arbitrary_Modint operator-() const { return Arbitrary_Modint(-x); } Arbitrary_Modint &operator++() { x++; if (x == MOD) x = 0; return *this; } Arbitrary_Modint &operator--() { if (x == 0) x = MOD; x--; return *this; } Arbitrary_Modint operator++(int) { Arbitrary_Modint result = *this; ++*this; return result; } Arbitrary_Modint operator--(int) { Arbitrary_Modint result = *this; --*this; return result; } friend Arbitrary_Modint operator+(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) { return Arbitrary_Modint(lhs) += rhs; } friend Arbitrary_Modint operator-(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) { return Arbitrary_Modint(lhs) -= rhs; } friend Arbitrary_Modint operator*(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) { return Arbitrary_Modint(lhs) *= rhs; } friend Arbitrary_Modint operator/(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) { return Arbitrary_Modint(lhs) /= rhs; } friend Arbitrary_Modint operator%(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) { assert(rhs.x == 0); return Arbitrary_Modint(lhs); } bool operator==(const Arbitrary_Modint &p) const { return x == p.x; } bool operator!=(const Arbitrary_Modint &p) const { return x != p.x; } bool operator<(const Arbitrary_Modint &rhs) { return x < rhs.x; } bool operator<=(const Arbitrary_Modint &rhs) { return x <= rhs.x; } bool operator>(const Arbitrary_Modint &rhs) { return x > rhs.x; } bool operator>=(const Arbitrary_Modint &rhs) { return x >= rhs.x; } Arbitrary_Modint inverse() const { int a = x, b = MOD, u = 1, v = 0, t; while (b > 0) { t = a / b; a -= t * b; u -= t * v; std::swap(a, b); std::swap(u, v); } return Arbitrary_Modint(u); } Arbitrary_Modint pow(int64_t k) const { Arbitrary_Modint ret(1); Arbitrary_Modint y(x); while (k > 0) { if (k & 1) ret *= y; y *= y; k >>= 1; } return ret; } friend std::ostream &operator<<(std::ostream &os, const Arbitrary_Modint &p) { return os << p.x; } friend std::istream &operator>>(std::istream &is, Arbitrary_Modint &p) { int64_t y; is >> y; p = Arbitrary_Modint(y); return (is); } static int get_mod() { return MOD; } }; int Arbitrary_Modint::MOD = 998244353; using modint9 = Modint<998244353>; using modint1 = Modint<1000000007>; using modint = Arbitrary_Modint; struct HLD { int n, path; std::vector> edges; std::vector siz; std::vector par; std::vector depth; std::vector path_ind; std::vector path_root; std::vector heavy_child; std::vector isheavy; std::vector L; std::vector R; HLD(int n) : n(n) { edges.resize(n); siz.assign(n, -1); par.assign(n, -1); depth.assign(n, -1); path_ind.assign(n, -1); heavy_child.assign(n, -1); isheavy.assign(n, false); L.assign(n, -1); R.assign(n, -1); } void read_edges(int indexed = 1) { int u, v; for (int i = 0; i < n - 1; i++) { std::cin >> u >> v; u -= indexed; v -= indexed; edges[u].push_back(v); edges[v].push_back(u); } } void add_edge(int u, int v) { edges[u].push_back(v); edges[v].push_back(u); } void build(int root = 0) { depth[root] = 0; std::stack st; std::vector route; st.push(root); route.push_back(root); while (!st.empty()) { int pos = st.top(); st.pop(); for (auto npos : edges[pos]) { if (depth[npos] == -1) { depth[npos] = depth[pos] + 1; par[npos] = pos; st.push(npos); route.push_back(npos); } } } reverse(route.begin(), route.end()); for (auto pos : route) { siz[pos] = 1; int ma = -1; for (auto npos : edges[pos]) { if (depth[npos] > depth[pos]) siz[pos] += siz[npos]; if (siz[npos] > ma) { ma = siz[npos]; heavy_child[pos] = npos; } } if (heavy_child[pos] != -1) isheavy[heavy_child[pos]] = true; } isheavy[root] = true; path = 0; st.push(~root); st.push(root); path_root.push_back(root); int cc = 0; while (!st.empty()) { int pos = st.top(); st.pop(); if (pos >= 0) { L[pos] = cc++; if (!isheavy[pos]) { path++; path_root.push_back(pos); } path_ind[pos] = path; for (auto npos : edges[pos]) { if (npos == par[pos] || npos == heavy_child[pos]) continue; st.push(~npos); st.push(npos); } if (heavy_child[pos] != -1) { int npos = heavy_child[pos]; st.push(~npos); st.push(npos); } } else { pos = ~pos; R[pos] = cc; } } } std::vector> get_path(int u, int v) { std::vector ll; std::vector rr; ll.push_back(u); rr.push_back(v); while (path_ind[u] != path_ind[v]) { if (depth[path_root[path_ind[u]]] >= depth[path_root[path_ind[v]]]) { u = path_root[path_ind[u]]; ll.push_back(u); u = par[u]; ll.push_back(u); } else { v = path_root[path_ind[v]]; rr.push_back(v); v = par[v]; rr.push_back(v); } } reverse(rr.begin(), rr.end()); ll.insert(ll.end(), rr.begin(), rr.end()); int n = ll.size(); std::vector> res(n / 2); for (int i = 0; i < n; i += 2) { res[i / 2] = {ll[i], ll[i + 1]}; } return res; } int lca(int u, int v) { while (path_ind[u] != path_ind[v]) { if (depth[path_root[path_ind[u]]] >= depth[path_root[path_ind[v]]]) u = par[path_root[path_ind[u]]]; else v = par[path_root[path_ind[v]]]; } return (depth[u] <= depth[v]) ? u : v; } int dist(int u, int v) { int p = lca(u, v); return depth[u] + depth[v] - 2 * depth[p]; } template std::vector reorder(std::vector &A, bool rev = false) { assert(int(A.size()) == n); std::vector ret(n); for (int i = 0; i < n; i++) { ret[L[i]] = A[i]; } if (rev) reverse(ret.begin(), ret.end()); return ret; } }; using mint = modint1; struct S { mint x00; mint x01; mint x10; mint x11; }; S op(S l, S r) { return S{l.x00 * r.x00 + l.x01 * r.x10, l.x00 * r.x01 + l.x01 * r.x11, l.x10 * r.x00 + l.x11 * r.x10, l.x10 * r.x01 + l.x11 * r.x11}; } S e() { return S{1, 0, 0, 1}; } void solve() { INT(n); HLD hld(2 * n - 1); fori(i, n - 1) { INT(u, v); hld.add_edge(u, i + n); hld.add_edge(v, i + n); } hld.build(0); segtree seg(2 * n - 1); INT(Q); fori(Q) { CHAR(t); if (t == 'x') { INT(i, x00, x01, x10, x11); i += n; seg.set(hld.L[i], S{x00, x01, x10, x11}); } else { INT(i, j); S ans = e(); for (auto [u, v] : hld.get_path(i, j)) { u = hld.L[u]; v = hld.L[v]; ans = op(ans, seg.prod(u, v + 1)); auto res = seg.prod(u, v + 1); } print(ans.x00, ans.x01, ans.x10, ans.x11); } } } int main() { #ifndef INTERACTIVE std::cin.tie(0)->sync_with_stdio(0); #endif // std::cout << std::fixed << std::setprecision(12); int t; t = 1; // std::cin >> t; while (t--) solve(); return 0; } // // #pragma GCC target("avx2") // // #pragma GCC optimize("O3") // // #pragma GCC optimize("unroll-loops") // // #define INTERACTIVE // // #include "kyopro-cpp/template.hpp" // // #include "data_structure/segTree.hpp" // #include "misc/Modint.hpp" // #include "tree/HLD.hpp" // using mint = modint1; // // struct S { // mint x00; // mint x01; // mint x10; // mint x11; // }; // S op(S l, S r) { // return S{l.x00 * r.x00 + l.x01 * r.x10, l.x00 * r.x01 + l.x01 * r.x11, // l.x10 * r.x00 + l.x11 * r.x10, l.x10 * r.x01 + l.x11 * r.x11}; // } // S e() { // return S{1, 0, 0, 1}; // } // // void solve() { // INT(n); // HLD hld(2 * n - 1); // fori(i, n - 1) { // INT(u, v); // hld.add_edge(u, i + n); // hld.add_edge(v, i + n); // } // hld.build(0); // segtree seg(2 * n - 1); // INT(Q); // fori(Q) { // CHAR(t); // if (t == 'x') { // INT(i, x00, x01, x10, x11); // i += n; // seg.set(hld.L[i], S{x00, x01, x10, x11}); // } else { // INT(i, j); // S ans = e(); // for (auto [u, v] : hld.get_path(i, j)) { // u = hld.L[u]; // v = hld.L[v]; // // ans = op(ans, seg.prod(u, v + 1)); // auto res = seg.prod(u, v + 1); // } // print(ans.x00, ans.x01, ans.x10, ans.x11); // } // } // } // // int main() { // #ifndef INTERACTIVE // std::cin.tie(0)->sync_with_stdio(0); // #endif // // std::cout << std::fixed << std::setprecision(12); // int t; // t = 1; // // std::cin >> t; // while (t--) solve(); // return 0; // }