#if __INCLUDE_LEVEL__ == 0 #include __BASE_FILE__ using Mint = atcoder::modint998244353; Comb comb; struct D { // vector cnt; array cnt{}; int mask = 1; void add(int x) { // if (x >= Sz(cnt)) { // cnt.resize(x + 1); // } if (cnt[x]++ == 0) { mask |= 1 << x; } } void remove(int x) { if (--cnt[x] == 0) { mask &= ~(1 << x); } } int get() const { return __bit_width(mask) - 1; } }; void Solve() { int n; IN(n); vector a(n); IN(a); int A = ranges::max(a); HldTree g(n); for (int _ : Rep(0, n - 1)) { int i, j; IN(i, j); --i, --j; g.add_edge({i, j, 1}); } g.build(0); linear_sieve::init(A); for (int i : Rep1(2, A)) { int prv = -1; int len = 0; for (int p : linear_sieve::factor(i)) { if (p != prv) { if (prv != -1) { CsrArray>::Add(i, {prv, len}); } prv = p; len = 1; } else { ++len; } } CsrArray>::Add(i, {prv, len}); } auto factors = CsrArray>::Build(A + 1); for (int p : linear_sieve::primes) { int prod = 1; for (int e = 0;; ++e) { CsrArray::Add(p, prod); if (prod > A / p) { break; } prod *= p; } } auto pw = CsrArray::Build(A + 1); Mint ans = 1; vector ds(A + 1); vector cnt(A + 1); auto add = [&](int x) { if (cnt[x]++ == 0) { for (auto [p, e] : factors[x]) { ans *= comb.Inv(pw[p][ds[p].get()]); ds[p].add(e); ans *= pw[p][ds[p].get()]; } } }; auto remove = [&](int x) { if (--cnt[x] == 0) { for (auto [p, e] : factors[x]) { ans *= comb.Inv(pw[p][ds[p].get()]); ds[p].remove(e); ans *= pw[p][ds[p].get()]; } } }; vector out(n); int L = 0; int R = 0; for (int i : g.order) { int l = g.in[i]; int r = g.out[i]; while (L > l) { --L; add(a[g.order[L]]); } while (R < r) { add(a[g.order[R]]); ++R; } while (L < l) { remove(a[g.order[L]]); ++L; } while (R > r) { --R; remove(a[g.order[R]]); } out[i] = ans; } ranges::for_each(out, LIFT(OUT)); } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); Solve(); } #elif __INCLUDE_LEVEL__ == 1 #include #include template class Comb { public: Comb() = default; explicit Comb(int n) { Reserve(n); } void Reserve(int n) { const int sz = static_cast(fact_.size()); if (n < sz) { return; } fact_.resize(n + 1); const int nsz = static_cast(fact_.capacity()); fact_.resize(nsz); fact_inv_.resize(nsz); for (int i = sz; i < nsz; ++i) { fact_[i] = T(i) * fact_[i - 1]; } fact_inv_.back() = T(1) / fact_.back(); for (int i = nsz; --i > sz;) { fact_inv_[i - 1] = fact_inv_[i] * T(i); } } T Fact(int n) { assert(n >= 0); Reserve(n); return fact_[n]; } T FactInv(int n) { if (n < 0) { return T(0); } Reserve(n); return fact_inv_[n]; } T FactRatio(int a, int b) { if (a >= 0) { return Fact(a) * FactInv(b); } assert(b < 0); const T t = FactRatio(~b, ~a); return (a - b) % 2 == 0 ? t : -t; } T Inv(int n) { assert(n != 0); return FactRatio(n - 1, n); } T Prod(std::ranges::iota_view r) { return FactRatio(r.end()[-1], r[-1]); } T ProdInv(std::ranges::iota_view r) { assert(r[0] > 0 || r.end()[-1] < 0); return FactRatio(r[-1], r.end()[-1]); } T Perm(int n, int k) { assert(n >= 0 ? true : k > n); return FactRatio(n, n - k); } T PermInv(int n, int k) { assert(n >= 0 ? k <= n : true); return FactRatio(n - k, n); } T Binom(int n, int k) { k = std::max(k, n - k); return Perm(n, k) * FactInv(k); } T BinomInv(int n, int k) { assert(n >= 0 ? 0 <= k && k <= n : 0 <= k || k <= n); k = std::max(k, n - k); return PermInv(n, k) * Fact(k); } T Multinom(std::span ks) { if (ks.size() < 2) { return T(1); } const int n = std::reduce(ks.begin(), ks.end()); const int& min_k = *std::ranges::min_element(ks); T ret = FactRatio(n, min_k); for (const int& k : ks) { if (&k != &min_k) { ret *= FactInv(k); } } return ret; } template requires(... && std::same_as) T Multinom(Ks... ks) { return Multinom(std::initializer_list{ks...}); } T MultinomInv(std::span ks) { if (ks.size() < 2) { return T(1); } const int n = std::reduce(ks.begin(), ks.end()); const int& min_k = *std::ranges::min_element(ks); assert(n >= 0 ? min_k >= 0 : std::ranges::all_of(ks, [&](auto& k) { return &k == &min_k || k >= 0; })); T ret = FactRatio(min_k, n); for (const int& k : ks) { if (&k != &min_k) { ret *= Fact(k); } } return ret; } template requires(... && std::same_as) T MultinomInv(Ks... ks) { return MultinomInv(std::initializer_list{ks...}); } T Homogeneous(int n, int k) { return Binom(n + k - 1, k); } T Catalan(int n) { assert(n >= 0); return Fact(2 * n) * FactInv(n) * FactInv(n + 1); } T Catalan(int n, int k) { assert(0 <= k && k <= n); return T(n - k + 1) * Fact(n + k) * FactInv(n + 1) * FactInv(k); } private: std::vector fact_{T(1)}; std::vector fact_inv_{T(1)}; }; template class CsrArray { public: static void Reserve(int m) { buf_.reserve(m); } static void Add(int i, T x) { buf_.emplace_back(i, std::move(x)); } static CsrArray Build(int n) { CsrArray ret; ret.pos_.resize(n + 1); for (int i : buf_ | std::views::keys) { ++ret.pos_[i]; } std::partial_sum(ret.pos_.begin(), ret.pos_.end(), ret.pos_.begin()); ret.data_.resize(ret.pos_[n]); for (auto& [i, x] : buf_ | std::views::reverse) { ret.data_[--ret.pos_[i]] = std::move(x); } buf_.clear(); return ret; } int size() const { return int(pos_.size()) - 1; } auto operator[](int i) { return std::span(data_.data() + pos_[i], data_.data() + pos_[i + 1]); } auto operator[](int i) const { return std::span(data_.data() + pos_[i], data_.data() + pos_[i + 1]); } private: static thread_local inline std::vector> buf_; std::vector data_; std::vector pos_; }; template concept MyRange = std::ranges::range && !std::convertible_to; template concept MyTuple = std::__is_tuple_like::value && !MyRange; namespace std { istream& operator>>(istream& is, MyRange auto&& r) { for (auto&& e : r) is >> e; return is; } istream& operator>>(istream& is, MyTuple auto&& t) { apply([&](auto&... xs) { (is >> ... >> xs); }, t); return is; } ostream& operator<<(ostream& os, MyRange auto&& r) { auto sep = ""; for (auto&& e : r) os << exchange(sep, " ") << e; return os; } ostream& operator<<(ostream& os, MyTuple auto&& t) { auto sep = ""; apply([&](auto&... xs) { ((os << exchange(sep, " ") << xs), ...); }, t); return os; } template * = nullptr> istream& operator>>(istream& is, T& x) { int v; is >> v; x = T::raw(v); return is; } template * = nullptr> ostream& operator<<(ostream& os, const T& x) { return os << x.val(); } } // namespace std struct Graph { struct Edge { int src, dst; int64_t cost; int other(int v) const { __glibcxx_assert(v == src or v == dst); return src ^ dst ^ v; } }; std::vector edges; std::vector>> adj; Graph() {} explicit Graph(int n) : adj(n) {} int n() const { return std::size(adj); } int m() const { return std::size(edges); } int add_edge(const Edge& e, bool directed) { __glibcxx_assert(0 <= e.src and e.src < n()); __glibcxx_assert(0 <= e.dst and e.dst < n()); int id = m(); edges.push_back(e); adj[e.src].emplace_back(e.dst, id); if (not directed) adj[e.dst].emplace_back(e.src, id); return id; } }; struct DfsTree : Graph { using T = decltype(Edge::cost); std::vector root; std::vector pv; std::vector pe; std::vector order; std::vector in; std::vector out; std::vector sub; std::vector depth; std::vector min_depth; std::vector dist; std::vector last; int num_trials; DfsTree() {} explicit DfsTree(int n) : Graph(n), root(n, -1), pv(n, -1), pe(n, -1), in(n, -1), out(n, -1), sub(n, -1), depth(n, -1), min_depth(n, -1), dist(n, std::numeric_limits::max()), last(n, -1), num_trials(0) {} int add_edge(const Edge& e) { return Graph::add_edge(e, false); } void dfs(int r, bool clear_order = true) { __glibcxx_assert(0 <= r and r < n()); root[r] = r; pv[r] = -1; pe[r] = -1; if (clear_order) order.clear(); depth[r] = 0; dist[r] = T{}; dfs_impl(r); ++num_trials; } void dfs_all() { std::fill(std::begin(root), std::end(root), -1); for (int v = 0; v < n(); ++v) if (root[v] == -1) dfs(v, v == 0); } int deeper(int id) const { __glibcxx_assert(0 <= id and id < m()); int a = edges[id].src; int b = edges[id].dst; return depth[a] < depth[b] ? b : a; } bool is_tree_edge(int id) const { __glibcxx_assert(0 <= id and id < m()); return id == pe[deeper(id)]; } bool is_ancestor(int u, int v) const { __glibcxx_assert(0 <= u and u < n()); __glibcxx_assert(0 <= v and v < n()); return in[u] <= in[v] and out[v] <= out[u]; } private: void dfs_impl(int v) { in[v] = std::size(order); order.push_back(v); sub[v] = 1; min_depth[v] = depth[v]; last[v] = num_trials; for (auto&& [u, id] : adj[v]) { if (id == pe[v]) continue; if (last[u] == num_trials) { min_depth[v] = std::min(min_depth[v], depth[u]); continue; } root[u] = root[v]; pv[u] = v; pe[u] = id; depth[u] = depth[v] + 1; dist[u] = dist[v] + edges[id].cost; dfs_impl(u); sub[v] += sub[u]; min_depth[v] = std::min(min_depth[v], min_depth[u]); } out[v] = std::size(order); } }; struct HldTree : DfsTree { std::vector head; HldTree() {} explicit HldTree(int n) : DfsTree(n), head(n, -1) {} void build(int r, bool clear_order = true) { __glibcxx_assert(0 <= r and r < n()); dfs(r, clear_order); order.erase(std::end(order) - sub[r], std::end(order)); head[r] = r; build_impl(r); } void build_all() { std::fill(std::begin(root), std::end(root), -1); for (int v = 0; v < n(); ++v) if (root[v] == -1) build(v, v == 0); } int lca(int u, int v) const { __glibcxx_assert(0 <= u and u < n()); __glibcxx_assert(0 <= v and v < n()); __glibcxx_assert(root[u] == root[v]); while (true) { if (in[u] > in[v]) std::swap(u, v); if (head[u] == head[v]) return u; v = pv[head[v]]; } } int d(int u, int v) const { __glibcxx_assert(0 <= u and u < n()); __glibcxx_assert(0 <= v and v < n()); __glibcxx_assert(root[u] == root[v]); return depth[u] + depth[v] - 2 * depth[lca(u, v)]; } T distance(int u, int v) const { __glibcxx_assert(0 <= u and u < n()); __glibcxx_assert(0 <= v and v < n()); __glibcxx_assert(root[u] == root[v]); return dist[u] + dist[v] - 2 * dist[lca(u, v)]; } int la(int v, int d) const { __glibcxx_assert(0 <= v and v < n()); __glibcxx_assert(0 <= d and d <= depth[v]); while (depth[head[v]] > d) v = pv[head[v]]; return order[in[head[v]] + (d - depth[head[v]])]; } int next(int src, int dst) const { __glibcxx_assert(0 <= src and src < n()); __glibcxx_assert(0 <= dst and dst < n()); __glibcxx_assert(root[src] == root[dst]); __glibcxx_assert(src != dst); if (not is_ancestor(src, dst)) return pv[src]; return la(dst, depth[src] + 1); } int next(int src, int dst, int k) const { __glibcxx_assert(0 <= src and src < n()); __glibcxx_assert(0 <= dst and dst < n()); __glibcxx_assert(root[src] == root[dst]); __glibcxx_assert(k >= 0); int v = lca(src, dst); if (k <= depth[src] - depth[v]) return la(src, depth[src] - k); k -= depth[src] - depth[v]; __glibcxx_assert(k <= depth[dst] - depth[v]); return la(dst, depth[v] + k); } template void apply(int src, int dst, bool vertex, Function f) const { __glibcxx_assert(0 <= src and src < n()); __glibcxx_assert(0 <= dst and dst < n()); __glibcxx_assert(root[src] == root[dst]); int v = lca(src, dst); while (head[src] != head[v]) { f(in[src] + 1, in[head[src]]); src = pv[head[src]]; } if (vertex) f(in[src] + 1, in[v]); else if (src != v) f(in[src] + 1, in[v] + 1); auto rec = [&](auto self, int to) -> void { if (head[v] == head[to]) { if (v != to) f(in[v] + 1, in[to] + 1); return; } self(self, pv[head[to]]); f(in[head[to]], in[to] + 1); }; rec(rec, dst); } template int search(int src, int dst, bool vertex, Searcher f) const { __glibcxx_assert(0 <= src and src < n()); __glibcxx_assert(0 <= dst and dst < n()); __glibcxx_assert(root[src] == root[dst]); int res = -1; apply(src, dst, vertex, [&](int l, int r) { if (res != -1) return; int i = f(l, r); if (l > r) std::swap(l, r); if (l <= i and i < r) res = vertex ? order[i] : pe[order[i]]; }); return res; } private: void build_impl(int v) { in[v] = std::size(order); order.push_back(v); auto pos = std::partition(std::begin(adj[v]), std::end(adj[v]), [&](auto&& e) { return e.second == pe[e.first]; }); auto it = std::max_element(std::begin(adj[v]), pos, [&](auto&& a, auto&& b) { return sub[a.first] < sub[b.first]; }); if (it != std::begin(adj[v])) std::iter_swap(std::begin(adj[v]), it); std::partition(pos, std::end(adj[v]), [&](auto&& e) { return e.second == pe[v]; }); for (auto&& [u, id] : adj[v]) { if (id != pe[u]) break; head[u] = u == adj[v].front().first ? head[v] : u; build_impl(u); } out[v] = std::size(order); } }; namespace linear_sieve { std::vector primes, lpf; void init(int n) { if (n < int(std::size(lpf))) return; if (n < 2 * int(std::size(lpf))) n = 2 * std::size(lpf); lpf.resize(n + 1, -1); for (int d = 2; d <= n; ++d) { if (lpf[d] == -1) lpf[d] = d, primes.push_back(d); for (int p : primes) { if (p * d > n or p > lpf[d]) break; lpf[p * d] = p; } } } std::vector factor(int n) { __glibcxx_assert(n >= 1); std::vector res; for (init(n); n > 1; n /= res.back()) res.push_back(lpf[n]); return res; } } // namespace linear_sieve using namespace std; #define _ _ [[maybe_unused]] #define LIFT(f) ([&](auto&&... xs) -> decltype(auto) { return f(forward(xs)...); }) #define Rep(...) [](int l, int r) { return views::iota(min(l, r), r); }(__VA_ARGS__) #define Rep1(...) [](int l, int r) { return Rep(l, r + 1); }(__VA_ARGS__) #define IN(...) (cin >> forward_as_tuple(__VA_ARGS__)) #define OUT(...) (cout << forward_as_tuple(__VA_ARGS__) << '\n') #endif // __INCLUDE_LEVEL__ == 1