//#pragma warning(disable:4996) //#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include //#include //< in.txt > out.txt using namespace std; //std::ios::sync_with_stdio(false); //std::cin.tie(0); const long long MOD = 1e9 + 7; const long long INF = 1e18; typedef long long LL; typedef long double LD; typedef boost::multiprecision::cpp_int bigint; typedef pair PLL; typedef pair PI; typedef pair pdl; typedef pair pdd; typedef vector VLL; typedef vector VVLL; typedef vector VI; typedef vector> VVI; typedef unsigned long long ULL; template using pqueue = priority_queue, function>; template inline void chmin(T& a, T b) { a = min(a, b); } template inline void chmax(T& a, T b) { a = max(a, b); } void input(); void solve(); void daminput(); void naive(); void outputinput(); int main() { std::cin.tie(0); std::ios::sync_with_stdio(false); input(); //daminput(); solve(); //naive(); //outputinput(); return 0; } ////////////////////////////////////////////////// ////////////////////////////////////////////////// void input() { } void daminput() { } template class Matrix { public: vector> v; int H, W; Matrix(int h, int w) :H(h), W(w) { v.resize(h, vector(w, K(0))); } Matrix(vector& v0) { H = v0.size(); W = 1; v.resize(H, vector(1, K(0))); for (int y = 0; y < H; y++) { v[y][0] = v0[y]; } } Matrix() :H(0), W(0) {} void resize(int h, int w) { H = h; W = w; v.resize(H, vector(W, K(0))); } vector& operator[](int y) { return v[y]; } vector& back() { return v.back(); } Matrix& operator+=(Matrix& B); Matrix& operator-=(Matrix& B); Matrix& operator*=(Matrix& B); Matrix& operator*=(K k); Matrix& operator/=(K k); }; template Matrix operator+(Matrix& A, Matrix& B) { assert(A.H == B.H && A.W == B.W); int H = A.H; int W = A.W; Matrix C(H, W); for (int y = 0; y < H; y++) { for (int x = 0; x < W; x++) { C[y][x] = A[y][x] + B[y][x]; } } return C; } template Matrix operator-(Matrix& A, Matrix& B) { assert(A.H == B.H && A.W == B.W); int H = A.H; int W = A.W; Matrix C(H, W); for (int y = 0; y < H; y++) { for (int x = 0; x < W; x++) { C[y][x] = A[y][x] - B[y][x]; } } return C; } template Matrix operator*(Matrix& A, Matrix& B) { assert(A.W == B.H); int H = A.H; int W = B.W; Matrix C(H, W); for (int k = 0; k < A.W; k++) { for (int y = 0; y < H; y++) { for (int x = 0; x < W; x++) { C[y][x] += A[y][k] * B[k][x]; } } } return C; } template Matrix operator*(Matrix& A, K k) { int H = A.H; int W = A.W; Matrix C(H, W); for (int y = 0; y < A.H; y++) { for (int x = 0; x < A.W; x++) { C[y][x] = A[y][x] * k; } } return C; } template Matrix operator*(K k, Matrix& A) { int H = A.H; int W = A.W; Matrix C(H, W); for (int y = 0; y < A.H; y++) { for (int x = 0; x < A.W; x++) { C[y][x] = A[y][x] * k; } } return C; } template Matrix operator/(Matrix& A, K k) { int H = A.H; int W = A.W; Matrix C(H, W); for (int y = 0; y < A.H; y++) { for (int x = 0; x < A.W; x++) { C[y][x] = A[y][x] / k; } } return C; } template Matrix& Matrix::operator+=(Matrix& B) { assert(H == B.H && W == B.W); for (int y = 0; y < H; y++) { for (int x = 0; x < W; x++) { v[y][x] += B[y][x]; } } return *this; } template Matrix& Matrix::operator-=(Matrix& B) { assert(H == B.H && W == B.W); for (int y = 0; y < H; y++) { for (int x = 0; x < W; x++) { v[y][x] -= B[y][x]; } } return *this; } template Matrix& Matrix::operator*=(Matrix& B) { *this = *this * B; return *this; } template Matrix& Matrix::operator*=(K k) { for (int y = 0; y < H; y++) { for (int x = 0; x < W; x++) { v[y][x] *= k; } } return *this; } template Matrix& Matrix::operator/=(K k) { for (int y = 0; y < H; y++) { for (int x = 0; x < W; x++) { v[y][x] /= k; } } return *this; } template bool operator==(Matrix& A, Matrix& B) { if (A.H != B.H || A.W != B.W)return false; for (int y = 0; y < A.H; y++) { for (int x = 0; x < A.W; x++) { if (A[y][x] != B[y][x])return false; } } return true; } template bool operator!=(Matrix& A, Matrix& B) { return !(A == B); } template Matrix pow(Matrix& A, LL p) { assert(A.H == A.W); if (p == 1)return A; Matrix temp = pow(A, p >> 1); temp *= temp; if (p == 1) { temp *= A; } return temp; } //行列Aを階段行列に変換する //返り値:行列のランク template int ConvertToStair(Matrix& A) { int H = A.H; int W = A.W; int x = 0, y = 0; while (true) { if (x >= W || y >= H)break; if (A[y][x] == K()) { int yy = y + 1; for (; yy < H; yy++) { if (A[yy][x] != K()) { swap(A[yy], A[y]); for (int xx = x; xx < W; xx++) { A[yy][xx] *= K(-1); } break; } } if (yy == H) { x++; continue; } } for (int yy = y + 1; yy < H; yy++) { K f = A[yy][x] / A[y][x]; for (int xx = x; xx < W; xx++) { A[yy][xx] = A[yy][xx] - A[y][xx] * f; } } x++; y++; } return y; } //行列Aを階段行列に変換する //conv[y][x] := 元の行列A_xを何回加えて今のA_yにしたか //返り値:行列のランク template int ConvertToStair(Matrix& A, vector>& conv) { int H = A.H; int W = A.W; int x = 0, y = 0; conv.resize(H, vector(H, K())); for (int yy = 0; yy < H; yy++) { conv[yy][yy] = K(1); } while (true) { if (x >= W || y >= H)break; if (A[y][x] == K()) { int yy = y + 1; for (; yy < H; yy++) { if (A[yy][x] != K()) { swap(A[yy], A[y]); swap(conv[yy], conv[y]); for (int xx = x; xx < W; xx++) { A[yy][xx] *= K(-1); } for (int n = 0; n < H; n++) { conv[yy][n] *= K(-1); } break; } } if (yy == H) { x++; continue; } } for (int yy = y + 1; yy < H; yy++) { K f = A[yy][x] / A[y][x]; for (int xx = x; xx < W; xx++) { A[yy][xx] = A[yy][xx] - A[y][xx] * f; } for (int n = 0; n < H; n++) { conv[yy][n] -= conv[y][n] * f; } } x++; y++; } return y; } //行列式を求める template K Determinant(Matrix& A) { ConvertToStair(A); K ans(1); for (int y = 0; y < A.H; y++) { ans *= A[y][y]; } return ans; } //線型方程式を解く //返り値:解の有無 //particular:特殊解 //bases:解空間の基底 template bool SolveLinearEquations(Matrix& A, vector& B, vector>& bases, vector& particular) { int H = A.H; int W = A.W; int X = 0, Y = 0; //階段行列に変形 while (true) { if (X >= W || Y >= H)break; if (A[Y][X] == K()) { int y = Y + 1; for (; y < H; y++) { if (A[y][X] != K()) { swap(A[y], A[Y]); swap(B[y], B[Y]); break; } } if (y == H) { X++; continue; } } for (int y = Y + 1; y < H; y++) { K f = A[y][X] / A[Y][X]; for (int x = X; x < W; x++) { A[y][x] = A[y][x] - A[Y][x] * f; } B[y] -= B[Y] * f; } X++; Y++; } //元のAのランクと、AにBをくっつけた拡張行列のランクが等しいか確かめる for (int y = Y; y < H; y++) { if (B[y] != K(0)) { //解は存在しない return false; } } int rank = Y; bases.resize(W - rank, vector(W, K(0))); //右上三角行列を作るように列を取っていく particular.resize(W, K(0)); X = 0; Y = 0; VI use; //取る列 VI notuse; //取らない列 while (X < W && Y < rank) { if (A[Y][X] == K(0)) { notuse.push_back(X); X++; } else { use.push_back(X); X++; Y++; } } while (X < W) { notuse.push_back(X); X++; } //特殊解を求める for (int x : notuse) { particular[x] = K(0); } for (int y = rank - 1; y >= 0; y--) { K b = B[y]; for (int x = y + 1; x < rank; x++) { b -= A[y][use[x]] * particular[use[x]]; } particular[use[y]] = b / A[y][use[y]]; } //解空間の基底 for (int base = 0; base < W - rank; base++) { vector& v = bases[base]; for (int x : notuse) { v[x] = K(0); } v[notuse[base]] = K(1); for (int y = rank - 1; y >= 0; y--) { K b = -1 * A[y][notuse[base]]; for (int x = y + 1; x < rank; x++) { b -= A[y][use[x]] * v[use[x]]; } v[use[y]] = b / A[y][use[y]]; } } return true; } //線型方程式を解く //返り値:解空間の有無 //particular:特殊解 template bool SolveLinearEquations(Matrix& A, vector& B, vector& particular) { int H = A.H; int W = A.W; int X = 0, Y = 0; //階段行列に変形 while (true) { if (X >= W || Y >= H)break; if (A[Y][X] == K()) { int y = Y + 1; for (; y < H; y++) { if (A[y][X] != K()) { swap(A[y], A[Y]); swap(B[y], B[Y]); break; } } if (y == H) { X++; continue; } } for (int y = Y + 1; y < H; y++) { K f = A[y][X] / A[Y][X]; for (int x = X; x < W; x++) { A[y][x] = A[y][x] - A[Y][x] * f; } B[y] -= B[Y] * f; } X++; Y++; } //元のAのランクと、AにBをくっつけた拡張行列のランクが等しいか確かめる for (int y = Y; y < H; y++) { if (B[y] != K(0)) { //解は存在しない return false; } } int rank = Y; //右上三角行列を作るように列を取っていく particular.resize(W, K(0)); X = 0; Y = 0; VI use; //取る列 VI notuse; //取らない列 while (X < W && Y < rank) { if (A[Y][X] == K(0)) { notuse.push_back(X); X++; } else { use.push_back(X); X++; Y++; } } while (X < W) { notuse.push_back(X); X++; } //特殊解を求める for (int x : notuse) { particular[x] = K(0); } for (int y = rank - 1; y >= 0; y--) { K b = B[y]; for (int x = y + 1; x < rank; x++) { b -= A[y][use[x]] * particular[use[x]]; } particular[use[y]] = b / A[y][use[y]]; } return true; } template struct Gedge { int src, to; T cost; int id; Gedge(int s, int t, T c, int i = -1) :src(s), to(t), cost(c), id(i) {} Gedge(int t, T c) :src(-1), to(t), cost(c), id(-1) {} }; template using WeightedGraph = vector>>; using UnweightedGraph = vector>; template using Gedges = vector>; template struct TNode { int parent; VI childs; T cost; int id; TNode() :parent(-1), cost(0), id(-1) {}; }; template using Tree = vector>; template class HLD { public: Tree& tree; LL V; VLL depth; //各頂点が属するHeavy集合の深さ VLL top; //各頂点が属するHeavy集合の一番上の頂点 VLL in; //各頂点がEuler-Tourでどこにいるか VLL out; //各頂点の部分木の終わり HLD(Tree& t, LL root = 0) :tree(t) { V = t.size(); VLL subtrees(V, -1); //各部分木のサイズを求める { stack order; stack hold; hold.push(root); while (!hold.empty()) { LL cur = hold.top(); hold.pop(); order.push(cur); for (LL ch : tree[cur].childs) { hold.push(ch); } } while (!order.empty()) { LL cur = order.top(); order.pop(); subtrees[cur] = 1; for (int& ch : tree[cur].childs) { subtrees[cur] += subtrees[ch]; if (subtrees[ch] > subtrees[tree[cur].childs[0]]) { swap(ch, tree[cur].childs[0]); } } } } //HL分解 with eulertour { in.resize(V); out.resize(V); depth.resize(V); top.resize(V); LL cur = root; LL nextid = 0; dfs(cur, nextid); } } void dfs(LL cur, LL& nextind) { in[cur] = nextind++; for (auto ch : tree[cur].childs) { //0番目の子は同じHeavy集合 if (ch == tree[cur].childs[0]) { top[ch] = top[cur]; depth[ch] = depth[cur]; } //それ以外は新しいHeavy集合 else { top[ch] = ch; depth[ch] = depth[cur] + 1; } dfs(ch, nextind); } out[cur] = nextind - 1; } LL LCA(LL u, LL v) { //uの属するnode.depth >= vの属するnode.depthにする if (depth[u] < depth[v]) { swap(u, v); } while (depth[u] > depth[v]) { u = tree[top[u]].parent; } while (top[u] != top[v]) { u = tree[top[u]].parent; v = tree[top[v]].parent; } if (in[u] > in[v])return v; else return u; } }; template void SetTree(WeightedGraph& G, Tree& T, int root = 0) { int N = G.size(); T.resize(N); queue q; q.push(root); T[root].parent = -1; T[root].id = -1; T[root].cost = 0; while (!q.empty()) { int cur = q.front(); q.pop(); for (Gedge& e : G[cur]) { if (e.to == T[cur].parent)continue; T[e.to].parent = cur; T[cur].childs.push_back(e.to); T[e.to].id = e.id; T[e.to].cost = e.cost; q.push(e.to); } } } //TT(T,T):=モノイドの乗算 //require Monoid template class Segtree { private: vector seg; LL RN; typedef function TT; TT f; T te; public: Segtree(LL N, TT _f, T e) :te(e) { RN = 1; while (RN < N)RN *= 2; seg.resize(2 * RN, te); f = _f; } Segtree(vector& V, TT _f, T e) :te(e) { LL N = V.size(); RN = 1; while (RN < N)RN *= 2; seg.resize(2 * RN, te); f = _f; for (LL n = 0; n < N; n++) seg[RN + n] = V[n]; for (LL k = RN - 1; k >= 1; k--) { seg[k] = f(seg[2 * k], seg[2 * k + 1]); } } //set n-th as x(0 index!!!!!) void set(LL n, T x) { seg[RN + n] = x; n = (RN + n) / 2; while (n >= 1) { seg[n] = f(seg[2 * n], seg[2 * n + 1]); n /= 2; } } //change n-th number p to x*p(0 index!!!!!) void addl(LL n, T x) { seg[RN + n] = f(x, seg[RN + n]); n = (RN + n) / 2; while (n >= 1) { seg[n] = f(seg[2 * n], seg[2 * n + 1]); n /= 2; } } //change n-th number p to p*x(0 index!!!!!) void addr(LL n, T x) { seg[RN + n] = f(seg[RN + n], x); n = (RN + n) / 2; while (n >= 1) { seg[n] = f(seg[2 * n], seg[2 * n + 1]); n /= 2; } } //get [l,r] (0 index!!!!!) T get(LL l, LL r) { T ansl = te, ansr = te; r++; l += RN; r += RN; while (l < r) { if (l & 1) { ansl = f(ansl, seg[l]); l++; } if (r & 1) { r--; ansr = f(seg[r], ansr); } l >>= 1; r >>= 1; } return f(ansl, ansr); } //get n-th number(0 index!!!!!) T get(LL n) { return seg[RN + n]; } T operator[](LL n) { return seg[RN + n]; } }; class Modint { public: LL v; Modint(LL _v) { _v %= MOD; if (_v < 0)_v += MOD; v = _v; } Modint operator+=(Modint m); Modint operator-=(Modint m); Modint operator*=(Modint m); Modint operator/=(Modint m); friend ostream& operator<<(ostream& st, const Modint& m); friend istream& operator>>(istream& st, Modint& m); Modint() :v(0) {} static Modint one; }; bool operator==(Modint a, Modint b) { return a.v == b.v; } bool operator!=(Modint a, Modint b) { return a.v != b.v; } Modint Modint::one = Modint(1); template T pow(T& base, LL p) { if (p == 0)return T(); else if (p == 1)return base; T ret = pow(base, p / 2); ret *= ret; if (p & 1)ret *= base; return ret; } template T modpow(T base, LL p) { if (p == 0)return T(); else if (p == 1)return base; T ret = modpow(base, p / 2); ret *= ret; if (p & 1)ret *= base; return ret; } ostream& operator<<(ostream& st, const Modint& m) { cout << m.v; return st; } istream& operator>>(istream& st, Modint& m) { LL v; cin >> v; m.v = v % MOD; return st; } Modint operator+(Modint a, Modint b) { Modint r; r.v = a.v + b.v; if (r.v >= MOD)r.v -= MOD; return r; } Modint operator-(Modint a, Modint b) { Modint r; r.v = a.v - b.v; if (r.v < 0)r.v += MOD; return r; } Modint operator*(Modint a, Modint b) { return Modint((a.v * b.v) % MOD); } Modint operator+(Modint a, LL b) { return Modint(a.v + b); } Modint operator+(LL a, Modint b) { return Modint(a + b.v); } Modint operator-(Modint a, LL b) { return Modint(a.v - b); } Modint operator-(LL a, Modint b) { return Modint(a - b.v); } Modint operator*(Modint a, LL b) { return Modint(a.v * (b % MOD)); } Modint operator*(LL a, Modint b) { return Modint((a % MOD) * b.v); } Modint operator/(Modint a, Modint b) { return a * modpow(b, MOD - 2); } Modint Modint::operator+=(Modint m) { *this = *this + m; return *this; } Modint Modint::operator-=(Modint m) { *this = *this - m; return *this; } Modint Modint::operator*=(Modint m) { *this = *this * m; return *this; } Modint Modint::operator/=(Modint m) { *this *= modpow(m, MOD - 2); return *this; } //O(min(N-R,R)) Modint Comb(LL N, LL R) { if (R > N - R)return Comb(N, N - R); Modint ans((LL)1); for (LL n = N; n > N - R; n--) { ans *= Modint(n); } for (LL n = R; n >= 1; n--) { ans *= modpow(Modint(n), MOD - 2); } return ans; } void solve() { int N; cin >> N; WeightedGraph G(N); VI A(N-1), B(N-1); for (int n = 0; n < N - 1; n++) { int a, b; cin >> a >> b; A[n] = a; B[n] = b; G[a].push_back(Gedge(a, b, 0, n)); G[b].push_back(Gedge(b, a, 0, n)); } Tree T; SetTree(G, T, 0); HLD hld(T, 0); VI etov(N-1, -1); for (int n = 0; n < N - 1; n++) { int a = A[n]; int b = B[n]; if (T[a].parent == b) { etov[n] = a; } else { etov[n] = b; } } Matrix E(2, 2); E[0][0] = 1; E[0][1] = 0; E[1][0] = 0; E[1][1] = 1; Segtree> seg(N, [](Matrix a, Matrix b) { return a * b; }, E); int Q; cin >> Q; for (int q = 0; q < Q; q++) { string type; cin >> type; if (type[0] == 'x') { int i; Modint x00, x01, x10, x11; cin >> i >> x00 >> x01 >> x10 >> x11; i = etov[i]; Matrix after(2, 2); after[0][0] = x00; after[0][1] = x01; after[1][0] = x10; after[1][1] = x11; int iconv = hld.in[i]; seg.set(iconv, after); } else { int i, j; cin >> i >> j; Matrix ans = E; while (hld.top[i] != hld.top[j]) { int jtop = hld.top[j]; int jconv = hld.in[j]; int jtopconv = hld.in[jtop]; Matrix res = seg.get(jtopconv, jconv); ans = res * ans; j = jtop; j = T[j].parent; } while (j != i) { int jconv = hld.in[j]; Matrix res = seg.get(jconv); ans = res * ans; j = T[j].parent; } cout << ans[0][0] << " " << ans[0][1] << " " << ans[1][0] << " " << ans[1][1] << "\n"; } } } void naive() { } void outputinput() { }