#include #include #include #include using namespace std; #pragma warning (disable: 4996) class UnionFind { public: vector par; void init(int sz) { par.resize(sz, -1); } int root(int pos) { if (par[pos] == -1) return pos; par[pos] = root(par[pos]); return par[pos]; } void unite(int u, int v) { u = root(u); v = root(v); if (u == v) return; par[u] = v; } bool same(int u, int v) { if (root(u) == root(v)) return true; return false; } }; class RangeMin { public: int size_ = 1; vector dat; void init(int sz) { while (size_ <= sz) size_ *= 2; dat.resize(size_ * 2, (1 << 30)); } void update(int pos, int x) { pos += size_; dat[pos] = x; while (pos >= 2) { pos >>= 1; dat[pos] = min(dat[pos * 2], dat[pos * 2 + 1]); } } int query_(int l, int r, int a, int b, int u) { if (l <= a && b <= r) return dat[u]; if (r <= a || b <= l) return (1 << 30); int v1 = query_(l, r, a, (a + b) >> 1, u * 2); int v2 = query_(l, r, (a + b) >> 1, b, u * 2 + 1); return min(v1, v2); } int query(int l, int r) { return query_(l, r, 0, size_, 1); } }; // 入力ほか long long mod = 1000000007; long long N, M, Q; long long A[1 << 18], B[1 << 18], C[1 << 18]; long long X[1 << 18], Y[1 << 18], Z[1 << 18]; bool mst[1 << 18]; // 最小全域木 UnionFind UF; long long dist1[1 << 18]; long long dist2[1 << 18]; long long ord[1 << 18]; long long cl[1 << 18]; long long cr[1 << 18], cnts; long long par[1 << 18][24], pre[1 << 18]; vector> G[1 << 18], H[1 << 18]; vector I[1 << 18]; // 最小全域木以外の辺 RangeMin P1, P2; vector> tup1, tup2; int Important[1 << 18]; // 出力 long long Answer[1 << 18]; void dfs(int pos, long long dep1, long long dep2) { cnts++; cl[pos] = cnts; ord[cnts] = pos; dist1[pos] = dep1; dist2[pos] = dep2; for (int i = 0; i < G[pos].size(); i++) { if (cl[G[pos][i].first] >= 1) continue; par[G[pos][i].first][0] = pos; pre[G[pos][i].first] = G[pos][i].second; H[pos].push_back(G[pos][i]); dfs(G[pos][i].first, dep1 + 1, (dep2 + C[G[pos][i].second]) % mod); } cr[pos] = cnts; } int prevs(int pos, int x) { for (int i = 21; i >= 0; i--) { if (x >= (1 << i)) { pos = par[pos][i]; x -= (1 << i); } } return pos; } int lca(int u, int v) { if (dist1[u] > dist1[v]) swap(u, v); v = prevs(v, dist1[v] - dist1[u]); if (u == v) return u; for (int i = 21; i >= 0; i--) { if (par[u][i] != par[v][i]) { u = par[u][i]; v = par[v][i]; } } return par[u][0]; } long long getdist1(int u, int v) { int w = lca(u, v); return dist1[u] + dist1[v] - 2 * dist1[w]; } long long getdist2(int u, int v) { int w = lca(u, v); return (dist2[u] + dist2[v] - 2LL * dist2[w] + mod * mod) % mod; } int main() { // Step #1. 入力 scanf("%lld%lld", &N, &M); for (int i = 1; i <= M; i++) scanf("%lld%lld", &A[i], &B[i]); scanf("%lld", &Q); for (int i = 1; i <= Q; i++) scanf("%lld%lld%lld", &X[i], &Y[i], &Z[i]); C[1] = 2LL; for (int i = 2; i <= M; i++) C[i] = (2LL * C[i - 1]) % mod; // Step #2. 最小全域木を求める UF.init(N + 2); for (int i = 1; i <= M; i++) { if (UF.same(A[i], B[i]) == false) { UF.unite(A[i], B[i]); mst[i] = true; G[A[i]].push_back(make_pair(B[i], i)); G[B[i]].push_back(make_pair(A[i], i)); } } dfs(1, 0, 0); // Step #3. LCA を求める for (int i = 1; i <= 21; i++) { for (int j = 1; j <= N; j++) par[j][i] = par[par[j][i - 1]][i - 1]; } for (int i = 1; i <= M; i++) { if (mst[i] == true) continue; I[A[i]].push_back(i); I[B[i]].push_back(i); } // Step #4. 重要な辺を求める P1.init(N + 2); P2.init(N + 2); for (int i = 1; i <= M; i++) { if (mst[i] == true) { int idx = A[i]; if (dist1[A[i]] < dist1[B[i]]) idx = B[i]; tup1.push_back(make_tuple(cl[idx], -i, cr[idx])); tup2.push_back(make_tuple(cr[idx], i, cl[idx])); } if (mst[i] == false) { int dl = cl[A[i]], dr = cl[B[i]]; if (dl > dr) swap(dl, dr); tup1.push_back(make_tuple(dl, i, dr)); tup2.push_back(make_tuple(dr, -i, dl)); } } sort(tup1.begin(), tup1.end()); sort(tup2.begin(), tup2.end()); reverse(tup2.begin(), tup2.end()); for (int i = 1; i <= M; i++) Important[i] = (1 << 30); for (int i = 0; i < tup1.size(); i++) { int p1 = get<0>(tup1[i]), p2 = get<2>(tup1[i]), idx = get<1>(tup1[i]); if (idx < 0) { int ret = P1.query(p1, p2 + 1); Important[-idx] = min(Important[-idx], ret); } else { int rem = P1.dat[p2 + P1.size_]; P1.update(p2, min(rem, idx)); } } for (int i = 0; i < tup2.size(); i++) { int p1 = get<0>(tup2[i]), p2 = get<2>(tup2[i]), idx = get<1>(tup2[i]); if (idx >= 0) { int ret = P2.query(p2, p1 + 1); Important[idx] = min(Important[idx], ret); } else { int rem = P2.dat[p2 + P2.size_]; P2.update(p2, min(rem, -idx)); } } // Step #5. 答えを求める for (int i = 1; i <= Q; i++) { int d1 = getdist1(X[i], A[Z[i]]) + 1 + getdist1(B[Z[i]], Y[i]); int d2 = getdist1(X[i], B[Z[i]]) + 1 + getdist1(A[Z[i]], Y[i]); int d3 = getdist1(X[i], Y[i]); if ((d1 != d3 && d2 != d3) || mst[Z[i]] == false) { Answer[i] = getdist2(X[i], Y[i]); Answer[i] %= mod; } else if (Important[Z[i]] == (1 << 30)) { Answer[i] = -1; } else { int idx = Important[Z[i]]; int e1 = getdist1(X[i], A[idx]) + 1 + getdist1(B[idx], Y[i]); int e2 = getdist1(X[i], B[idx]) + 1 + getdist1(A[idx], Y[i]); if (e1 <= e2) { Answer[i] = getdist2(X[i], A[idx]) + C[idx] + getdist2(B[idx], Y[i]); Answer[i] %= mod; } else { Answer[i] = getdist2(X[i], B[idx]) + C[idx] + getdist2(A[idx], Y[i]); Answer[i] %= mod; } } } // Step #6. 出力 for (int i = 1; i <= Q; i++) { printf("%lld\n", Answer[i]); } return 0; }