#include using namespace std; #define ll long long // #define TEST const ll mod = 1000000007LL; struct Matrix { ll e00, e01, e10, e11; Matrix() { e00 = e11 = 1; e01 = e10 = 0; } Matrix(ll e00, ll e01, ll e10, ll e11) : e00(e00), e01(e01), e10(e10), e11(e11) {} Matrix operator *(Matrix a) { return Matrix( (e00 * a.e00 % mod + e01 * a.e10 % mod) % mod, (e00 * a.e01 % mod + e01 * a.e11 % mod) % mod, (e10 * a.e00 % mod + e11 * a.e10 % mod) % mod, (e10 * a.e01 % mod + e11 * a.e11 % mod) % mod ); } }; template struct SegmentTree { private: int sz, n; vector data; function f; T identity_element; public: /* constructor */ SegmentTree( vector& v, // initial data T identity_element, // identity element function f // operation ) { sz = v.size(); n = 1; while (n < sz) n <<= 1; this->f = f; this->identity_element = identity_element; data.resize(2 * n - 1, identity_element); for (int i = 0; i < sz; ++i) data[i + n - 1] = v[i]; for (int i = n - 2; i >= 0; --i) data[i] = f(data[2 * i + 1], data[2 * i + 2]); } /* update query */ void update(int idx, const T val) { idx += n - 1; data[idx] = val; while (idx) { idx = (idx - 1) >> 1; data[idx] = f(data[2 * idx + 1], data[2 * idx + 2]); } } /* get query */ T get(int left, int right, int k = 0, int l = 0, int r = -1) { if (r < 0) r = n; if (r <= left || right <= l) return identity_element; if (left <= l && r <= right) return data[k]; T val_l = get(left, right, 2 * k + 1, l, (l + r) / 2); T val_r = get(left, right, 2 * k + 2, (l + r) / 2, r); return f(val_l, val_r); } }; template struct HLD { vector>> g; int n; vector subsz, depth, parent; vector> chain_edge; vector> chain_node; map chain_top, chain_id, id_in_chain; /* constructor */ HLD(vector>>& g) { this->g = g; n = g.size(); parent.resize(g.size()); subsz.resize(g.size()); depth.resize(g.size()); } /* init parent, depth, and subsz */ int dfs_sz(int s = 0, int p = -1, int dep = 0) { parent[s] = p; depth[s] = dep; int sz = 1; if (g[s].size() > 2 && g[s][0].first == p) swap(g[s][0], g[s][1]); // g[s][0] must be heavy for (int i = 0; i < g[s].size(); ++i) { if (g[s][i].first != p) { sz += dfs_sz(g[s][i].first, s, dep + 1); if (subsz[g[s][0].first] < subsz[g[s][i].first]) swap(g[s][0], g[s][i]); // g[s][0] must be heavy } } subsz[s] = sz; return sz; } /* HL Decomposition */ void dfs_hld(int s, int& cid) { chain_id[s] = cid; for (int i = 0; i < g[s].size(); ++i) { if (g[s][i].first != parent[s]) { if (i == 0) { chain_edge.resize(cid + 1); chain_node.resize(cid + 1); chain_edge[cid].push_back(g[s][i].second); chain_node[cid].push_back(g[s][i].first); id_in_chain[g[s][i].first] = chain_edge[cid].size(); dfs_hld(g[s][i].first, cid); } else { ++cid; chain_edge.resize(cid + 1); chain_node.resize(cid + 1); chain_edge[cid].push_back(g[s][i].second); chain_node[cid].push_back(g[s][i].first); id_in_chain[g[s][i].first] = chain_edge[cid].size(); dfs_hld(g[s][i].first, cid); } } } } /* the number of chain */ int chain_number() { return chain_node.size(); } /* find chain_top */ void find_chain_top() { for (int i = 0; i < chain_number(); ++i) chain_top[i] = parent[chain_node[i][0]]; } /* for test */ void show() { #ifdef TEST for (int i = 0; i < chain_number(); ++i) { cout << "chain id : " << i << endl; cout << " " << chain_top[i]; for (int j = 0; j < chain_edge[i].size(); ++j) cout << "-" << chain_node[i][j]; cout << endl; } for (int i = 0; i < n; ++i) { cout << "node : " << i << endl; cout << " chain : " << chain_id[i] << ", id_in_chain : " << id_in_chain[i] << endl; } #endif } vector> segs; vector> rev_segs; /* build */ void build() { dfs_sz(); int cid = 0; dfs_hld(0, cid); find_chain_top(); /* 【TODO】*/ // セグ木の準備等 for (int i = 0; i < chain_number(); ++i) { segs.push_back( SegmentTree( chain_edge[i], Matrix(), [](Matrix a, Matrix b) {return b * a; } ) ); rev_segs.push_back( SegmentTree( chain_edge[i], Matrix(), [](Matrix a, Matrix b) {return a * b; } ) ); } } /* find lca */ int LCA(int s, int t) { if (chain_id[s] < chain_id[t]) swap(s, t); while (chain_id[s] != chain_id[t]) { s = chain_top[chain_id[s]]; if (chain_id[s] < chain_id[t]) swap(s, t); } if (depth[s] < depth[t]) return s; return t; } /* sub query */ T query_in_chain(int cid, int s, int t) { // s <= t, [s, t] return segs[cid].get(s, t + 1); } T query_in_chain_reverse(int cid, int s, int t) { // t <= s, [t, s] // return query_in_chain(int cid, int t, int s); return rev_segs[cid].get(t, s + 1); } void chain_update(int cid, int id, T d) { segs[cid].update(id, d); rev_segs[cid].update(id, d); } T merge(T l, T r) { return r * l; } /* edge query */ T edge_query(int s, int t, T ei) { int lca = LCA(s, t); // s to lca T left = ei; while (s != lca) { if (chain_id[s] != chain_id[lca]) { T tmp = query_in_chain_reverse( chain_id[s], id_in_chain[s] - 1, 0 ); left = merge(left, tmp); s = chain_top[chain_id[s]]; } else { T tmp = query_in_chain_reverse( chain_id[s], id_in_chain[s] - 1, id_in_chain[lca] ); left = merge(left, tmp); s = lca; } } // lca to t T right = ei; while (t != lca) { if (chain_id[t] != chain_id[lca]) { T tmp = query_in_chain( chain_id[t], 0, id_in_chain[t] - 1 ); right = merge(tmp, right); t = chain_top[chain_id[t]]; } else { T tmp = query_in_chain( chain_id[t], id_in_chain[lca], id_in_chain[t] - 1 ); right = merge(tmp, right); t = lca; } } return merge(left, right); } /* edge update query */ void update(int s, int t, T d) { if (depth[s] >= depth[t]) swap(s, t); if (chain_id[s] == chain_id[t]) chain_update(chain_id[s], id_in_chain[s], d); else chain_update(chain_id[t], 0, d); } }; int main() { int n; cin >> n; vector>> g(n); vector> edge(n - 1); for (int i = 0; i < n - 1; ++i) { int a, b; cin >> a >> b; edge[i] = { a, b }; g[a].emplace_back(b, Matrix()); g[b].emplace_back(a, Matrix()); } HLD tree(g); tree.build(); tree.show(); int q; cin >> q; while (q--) { char c; cin >> c; if (c == 'x') { int i; ll x00, x01, x10, x11; cin >> i >> x00 >> x01 >> x10 >> x11; Matrix x; x.e00 = x00; x.e01 = x01; x.e10 = x10; x.e11 = x11; tree.update(edge[i].first, edge[i].second, x); } else { int i, j; cin >> i >> j; Matrix res = tree.edge_query(j, i, Matrix()); cout << res.e00 << " "; cout << res.e01 << " "; cout << res.e10 << " "; cout << res.e11 << endl; } } return 0; }