test/atcoder/abc248_g.test.cpp

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• Last update: 2025-08-08 18:52:16+09:00
• Problem: https://atcoder.jp/contests/abc248/tasks/abc248_g

Depends on

• グラフ (src/Graph/Graph.hpp)
• 重軽分解 (src/Graph/HeavyLightDecomposition.hpp)
• 全方位木DP (src/Graph/Rerooting.hpp)
• CSR 表現を用いた二次元配列 他 (src/Internal/ListRange.hpp)
• modintを扱うテンプレート (src/Internal/modint_traits.hpp)
• 剰余の高速化 (src/Internal/Remainder.hpp)
• Binary GCD (src/Math/binary_gcd.hpp)
• 逆元 ($\mathbb{Z}/m\mathbb{Z}$) (src/Math/mod_inv.hpp)
• ModInt (src/Math/ModInt.hpp)
• 約数配列 (src/NumberTheory/ArrayOnDivisors.hpp)
• 高速素因数分解など (src/NumberTheory/Factors.hpp)
• 素数判定 (src/NumberTheory/is_prime.hpp)

Code

// competitive-verifier: IGNORE
// competitive-verifier: PROBLEM https://atcoder.jp/contests/abc248/tasks/abc248_g
// competitive-verifier: TLE 3
// competitive-verifier: MLE 2048
#include <iostream>
#include <vector>
#include "src/Math/ModInt.hpp"
#include "src/Graph/Graph.hpp"
#include "src/Graph/Rerooting.hpp"
#include "src/NumberTheory/ArrayOnDivisors.hpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 using Mint= ModInt<998244353>;
 int n;
 cin >> n;
 vector<int> A(n);
 Mint sum= 0;
 for (int &a: A) cin >> a, sum+= a;
 Graph g(n, n - 1);
 for (auto &e: g) cin >> e, --e;
 using T= ArrayOnDivisors<int, pair<int, Mint>>;
 auto put_edge= [&](int v, int, const T &dat) {
  T ret(A[v]);
  for (auto &&[d, a]: dat) {
   auto &[l0, l1]= ret[gcd(d, A[v])];
   auto [r0, r1]= a;
   l1+= r1;
   l0+= r0;
  }
  return ret;
 };
 auto op= [&](const T &l, const T &r) {
  if (l.size() == 0) return r;
  if (r.size() == 0) return l;
  auto ret= l;
  for (auto &[d, a]: ret) {
   auto &[l0, l1]= a;
   auto [r0, r1]= r[d];
   l1+= r1;
   l0+= r0;
  }
  return ret;
 };
 auto put_vertex= [&](int v, T dat) {
  if (dat.size() == 0) dat= T(A[v]);
  dat[A[v]].first+= 1;
  for (auto &[d, x]: dat) x.second+= x.first;
  return dat;
 };
 Mint ans= 0;
 for (auto dat: Rerooting<T>(g, put_edge, op, T(), put_vertex))
  for (auto &&[d, x]: dat) ans+= x.second * d;
 ans-= sum, ans/= 2;
 cout << ans << '\n';
 return 0;
}

#line 1 "test/atcoder/abc248_g.test.cpp"
// competitive-verifier: IGNORE
// competitive-verifier: PROBLEM https://atcoder.jp/contests/abc248/tasks/abc248_g
// competitive-verifier: TLE 3
// competitive-verifier: MLE 2048
#include <iostream>
#include <vector>
#line 2 "src/Math/mod_inv.hpp"
#include <utility>
#include <type_traits>
#include <cassert>
template <class Uint> constexpr inline Uint mod_inv(Uint a, Uint mod) {
 std::make_signed_t<Uint> x= 1, y= 0, z= 0;
 for (Uint q= 0, b= mod, c= 0; b;) z= x, x= y, y= z - y * (q= a / b), c= a, a= b, b= c - b * q;
 return assert(a == 1), x < 0 ? mod - (-x) % mod : x % mod;
}
#line 2 "src/Internal/Remainder.hpp"
namespace math_internal {
using namespace std;
using u8= unsigned char;
using u32= unsigned;
using i64= long long;
using u64= unsigned long long;
using u128= __uint128_t;
struct MP_Na {  // mod < 2^32
 u32 mod;
 constexpr MP_Na(): mod(0) {}
 constexpr MP_Na(u32 m): mod(m) {}
 constexpr inline u32 mul(u32 l, u32 r) const { return u64(l) * r % mod; }
 constexpr inline u32 set(u32 n) const { return n; }
 constexpr inline u32 get(u32 n) const { return n; }
 constexpr inline u32 norm(u32 n) const { return n; }
 constexpr inline u32 plus(u64 l, u32 r) const { return l+= r, l < mod ? l : l - mod; }
 constexpr inline u32 diff(u64 l, u32 r) const { return l-= r, l >> 63 ? l + mod : l; }
};
template <class u_t, class du_t, u8 B> struct MP_Mo {  // mod < 2^32, mod < 2^62
 u_t mod;
 constexpr MP_Mo(): mod(0), iv(0), r2(0) {}
 constexpr MP_Mo(u_t m): mod(m), iv(inv(m)), r2(-du_t(mod) % mod) {}
 constexpr inline u_t mul(u_t l, u_t r) const { return reduce(du_t(l) * r); }
 constexpr inline u_t set(u_t n) const { return mul(n, r2); }
 constexpr inline u_t get(u_t n) const { return n= reduce(n), n >= mod ? n - mod : n; }
 constexpr inline u_t norm(u_t n) const { return n >= mod ? n - mod : n; }
 constexpr inline u_t plus(u_t l, u_t r) const { return l+= r, l < (mod << 1) ? l : l - (mod << 1); }
 constexpr inline u_t diff(u_t l, u_t r) const { return l-= r, l >> (B - 1) ? l + (mod << 1) : l; }
private:
 u_t iv, r2;
 static constexpr u_t inv(u_t n, int e= 6, u_t x= 1) { return e ? inv(n, e - 1, x * (2 - x * n)) : x; }
 constexpr inline u_t reduce(const du_t &w) const { return u_t(w >> B) + mod - ((du_t(u_t(w) * iv) * mod) >> B); }
};
using MP_Mo32= MP_Mo<u32, u64, 32>;
using MP_Mo64= MP_Mo<u64, u128, 64>;
struct MP_Br {  // 2^20 < mod <= 2^41
 u64 mod;
 constexpr MP_Br(): mod(0), x(0) {}
 constexpr MP_Br(u64 m): mod(m), x((u128(1) << 84) / m) {}
 constexpr inline u64 mul(u64 l, u64 r) const { return rem(u128(l) * r); }
 static constexpr inline u64 set(u64 n) { return n; }
 constexpr inline u64 get(u64 n) const { return n >= mod ? n - mod : n; }
 constexpr inline u64 norm(u64 n) const { return n >= mod ? n - mod : n; }
 constexpr inline u64 plus(u64 l, u64 r) const { return l+= r, l < (mod << 1) ? l : l - (mod << 1); }
 constexpr inline u64 diff(u64 l, u64 r) const { return l-= r, l >> 63 ? l + (mod << 1) : l; }
private:
 u64 x;
 constexpr inline u128 quo(const u128 &n) const { return (n * x) >> 84; }
 constexpr inline u64 rem(const u128 &n) const { return n - quo(n) * mod; }
};
template <class du_t, u8 B> struct MP_D2B1 {  // mod < 2^63, mod < 2^64
 u64 mod;
 constexpr MP_D2B1(): mod(0), s(0), d(0), v(0) {}
 constexpr MP_D2B1(u64 m): mod(m), s(__builtin_clzll(m)), d(m << s), v(u128(-1) / d) {}
 constexpr inline u64 mul(u64 l, u64 r) const { return rem((u128(l) * r) << s) >> s; }
 constexpr inline u64 set(u64 n) const { return n; }
 constexpr inline u64 get(u64 n) const { return n; }
 constexpr inline u64 norm(u64 n) const { return n; }
 constexpr inline u64 plus(du_t l, u64 r) const { return l+= r, l < mod ? l : l - mod; }
 constexpr inline u64 diff(du_t l, u64 r) const { return l-= r, l >> B ? l + mod : l; }
private:
 u8 s;
 u64 d, v;
 constexpr inline u64 rem(const u128 &u) const {
  u128 q= (u >> 64) * v + u;
  u64 r= u64(u) - (q >> 64) * d - d;
  if (r > u64(q)) r+= d;
  if (r >= d) r-= d;
  return r;
 }
};
using MP_D2B1_1= MP_D2B1<u64, 63>;
using MP_D2B1_2= MP_D2B1<u128, 127>;
template <class u_t, class MP> constexpr u_t pow(u_t x, u64 k, const MP &md) {
 for (u_t ret= md.set(1);; x= md.mul(x, x))
  if (k & 1 ? ret= md.mul(ret, x) : 0; !(k>>= 1)) return ret;
}
}
#line 3 "src/Internal/modint_traits.hpp"
namespace math_internal {
struct m_b {};
struct s_b: m_b {};
}
template <class mod_t> constexpr bool is_modint_v= std::is_base_of_v<math_internal::m_b, mod_t>;
template <class mod_t> constexpr bool is_staticmodint_v= std::is_base_of_v<math_internal::s_b, mod_t>;
#line 6 "src/Math/ModInt.hpp"
namespace math_internal {
template <class MP, u64 MOD> struct SB: s_b {
protected:
 static constexpr MP md= MP(MOD);
};
template <class U, class B> struct MInt: public B {
 using Uint= U;
 static constexpr inline auto mod() { return B::md.mod; }
 constexpr MInt(): x(0) {}
 template <class T, typename= enable_if_t<is_modint_v<T> && !is_same_v<T, MInt>>> constexpr MInt(T v): x(B::md.set(v.val() % B::md.mod)) {}
 constexpr MInt(__int128_t n): x(B::md.set((n < 0 ? ((n= (-n) % B::md.mod) ? B::md.mod - n : n) : n % B::md.mod))) {}
 constexpr MInt operator-() const { return MInt() - *this; }
#define FUNC(name, op) \
 constexpr MInt name const { \
  MInt ret; \
  return ret.x= op, ret; \
 }
 FUNC(operator+(const MInt & r), B::md.plus(x, r.x))
 FUNC(operator-(const MInt & r), B::md.diff(x, r.x))
 FUNC(operator*(const MInt & r), B::md.mul(x, r.x))
 FUNC(pow(u64 k), math_internal::pow(x, k, B::md))
#undef FUNC
 constexpr MInt operator/(const MInt &r) const { return *this * r.inv(); }
 constexpr MInt &operator+=(const MInt &r) { return *this= *this + r; }
 constexpr MInt &operator-=(const MInt &r) { return *this= *this - r; }
 constexpr MInt &operator*=(const MInt &r) { return *this= *this * r; }
 constexpr MInt &operator/=(const MInt &r) { return *this= *this / r; }
 constexpr bool operator==(const MInt &r) const { return B::md.norm(x) == B::md.norm(r.x); }
 constexpr bool operator!=(const MInt &r) const { return !(*this == r); }
 constexpr bool operator<(const MInt &r) const { return B::md.norm(x) < B::md.norm(r.x); }
 constexpr inline MInt inv() const { return mod_inv<U>(val(), B::md.mod); }
 constexpr inline Uint val() const { return B::md.get(x); }
 friend ostream &operator<<(ostream &os, const MInt &r) { return os << r.val(); }
 friend istream &operator>>(istream &is, MInt &r) {
  i64 v;
  return is >> v, r= MInt(v), is;
 }
private:
 Uint x;
};
template <u64 MOD> using MP_B= conditional_t < (MOD < (1 << 30)) & MOD, MP_Mo32, conditional_t < MOD < (1ull << 32), MP_Na, conditional_t<(MOD < (1ull << 62)) & MOD, MP_Mo64, conditional_t<MOD<(1ull << 41), MP_Br, conditional_t<MOD<(1ull << 63), MP_D2B1_1, MP_D2B1_2>>>>>;
template <u64 MOD> using ModInt= MInt < conditional_t<MOD<(1 << 30), u32, u64>, SB<MP_B<MOD>, MOD>>;
}
using math_internal::ModInt;
#line 4 "src/Internal/ListRange.hpp"
#include <iterator>
#line 6 "src/Internal/ListRange.hpp"
#define _LR(name, IT, CT) \
 template <class T> struct name { \
  using Iterator= typename std::vector<T>::IT; \
  Iterator bg, ed; \
  Iterator begin() const { return bg; } \
  Iterator end() const { return ed; } \
  size_t size() const { return std::distance(bg, ed); } \
  CT &operator[](int i) const { return bg[i]; } \
 }
_LR(ListRange, iterator, T);
_LR(ConstListRange, const_iterator, const T);
#undef _LR
template <class T> struct CSRArray {
 std::vector<T> dat;
 std::vector<int> p;
 size_t size() const { return p.size() - 1; }
 ListRange<T> operator[](int i) { return {dat.begin() + p[i], dat.begin() + p[i + 1]}; }
 ConstListRange<T> operator[](int i) const { return {dat.cbegin() + p[i], dat.cbegin() + p[i + 1]}; }
};
template <template <class> class F, class T> std::enable_if_t<std::disjunction_v<std::is_same<F<T>, ListRange<T>>, std::is_same<F<T>, ConstListRange<T>>, std::is_same<F<T>, CSRArray<T>>>, std::ostream &> operator<<(std::ostream &os, const F<T> &r) {
 os << '[';
 for (int _= 0, __= r.size(); _ < __; ++_) os << (_ ? ", " : "") << r[_];
 return os << ']';
}
#line 3 "src/Graph/Graph.hpp"
struct Edge: std::pair<int, int> {
 using std::pair<int, int>::pair;
 Edge &operator--() { return --first, --second, *this; }
 int to(int v) const { return first ^ second ^ v; }
 friend std::istream &operator>>(std::istream &is, Edge &e) { return is >> e.first >> e.second, is; }
};
struct Graph: std::vector<Edge> {
 size_t n;
 Graph(size_t n= 0, size_t m= 0): vector(m), n(n) {}
 size_t vertex_size() const { return n; }
 size_t edge_size() const { return size(); }
 size_t add_vertex() { return n++; }
 size_t add_edge(int s, int d) { return emplace_back(s, d), size() - 1; }
 size_t add_edge(Edge e) { return emplace_back(e), size() - 1; }
#define _ADJ_FOR(a, b) \
 for (auto [u, v]: *this) a; \
 for (size_t i= 0; i < n; ++i) p[i + 1]+= p[i]; \
 for (int i= size(); i--;) { \
  auto [u, v]= (*this)[i]; \
  b; \
 }
#define _ADJ(a, b) \
 vector<int> p(n + 1), c(size() << !dir); \
 if (!dir) { \
  _ADJ_FOR((++p[u], ++p[v]), (c[--p[u]]= a, c[--p[v]]= b)) \
 } else if (dir > 0) { \
  _ADJ_FOR(++p[u], c[--p[u]]= a) \
 } else { \
  _ADJ_FOR(++p[v], c[--p[v]]= b) \
 } \
 return {c, p}
 CSRArray<int> adjacency_vertex(int dir) const { _ADJ(v, u); }
 CSRArray<int> adjacency_edge(int dir) const { _ADJ(i, i); }
#undef _ADJ
#undef _ADJ_FOR
};
#line 2 "src/Graph/Rerooting.hpp"
#include <valarray>
#line 2 "src/Graph/HeavyLightDecomposition.hpp"
#include <array>
#line 5 "src/Graph/HeavyLightDecomposition.hpp"
class HeavyLightDecomposition {
 std::vector<int> P, PP, D, I, L, R;
public:
 HeavyLightDecomposition()= default;
 HeavyLightDecomposition(const Graph &g, int root= 0): HeavyLightDecomposition(g.adjacency_vertex(0), root) {}
 HeavyLightDecomposition(const CSRArray<int> &adj, int root= 0) {
  const int n= adj.size();
  P.assign(n, -2), PP.resize(n), D.resize(n), I.resize(n), L.resize(n), R.resize(n);
  auto f= [&, i= 0, v= 0, t= 0](int r) mutable {
   for (P[r]= -1, I[t++]= r; i < t; ++i)
    for (int u: adj[v= I[i]])
     if (P[v] != u) P[I[t++]= u]= v;
  };
  f(root);
  for (int r= 0; r < n; ++r)
   if (P[r] == -2) f(r);
  std::vector<int> Z(n, 1), nx(n, -1);
  for (int i= n, v; i--;) {
   if (P[v= I[i]] == -1) continue;
   if (Z[P[v]]+= Z[v]; nx[P[v]] == -1) nx[P[v]]= v;
   if (Z[nx[P[v]]] < Z[v]) nx[P[v]]= v;
  }
  for (int v= n; v--;) PP[v]= v;
  for (int v: I)
   if (nx[v] != -1) PP[nx[v]]= v;
  for (int v: I)
   if (P[v] != -1) PP[v]= PP[PP[v]], D[v]= D[P[v]] + 1;
  for (int i= n; i--;) L[I[i]]= i;
  for (int v: I) {
   int ir= R[v]= L[v] + Z[v];
   for (int u: adj[v])
    if (u != P[v] && u != nx[v]) L[u]= (ir-= Z[u]);
   if (nx[v] != -1) L[nx[v]]= L[v] + 1;
  }
  for (int i= n; i--;) I[L[i]]= i;
 }
 int to_seq(int v) const { return L[v]; }
 int to_vertex(int i) const { return I[i]; }
 size_t size() const { return P.size(); }
 int parent(int v) const { return P[v]; }
 int head(int v) const { return PP[v]; }
 int root(int v) const {
  for (v= PP[v];; v= PP[P[v]])
   if (P[v] == -1) return v;
 }
 bool connected(int u, int v) const { return root(u) == root(v); }
 // u is in v
 bool in_subtree(int u, int v) const { return L[v] <= L[u] && L[u] < R[v]; }
 int subtree_size(int v) const { return R[v] - L[v]; }
 int lca(int u, int v) const {
  for (;; v= P[PP[v]]) {
   if (L[u] > L[v]) std::swap(u, v);
   if (PP[u] == PP[v]) return u;
  }
 }
 int la(int v, int k) const {
  assert(k <= D[v]);
  for (int u;; k-= L[v] - L[u] + 1, v= P[u])
   if (L[v] - k >= L[u= PP[v]]) return I[L[v] - k];
 }
 int jump(int u, int v, int k) const {
  if (!k) return u;
  if (u == v) return -1;
  if (k == 1) return in_subtree(v, u) ? la(v, D[v] - D[u] - 1) : P[u];
  int w= lca(u, v), d_uw= D[u] - D[w], d_vw= D[v] - D[w];
  return k > d_uw + d_vw ? -1 : k <= d_uw ? la(u, k) : la(v, d_uw + d_vw - k);
 }
 int depth(int v) const { return D[v]; }
 int dist(int u, int v) const { return D[u] + D[v] - D[lca(u, v)] * 2; }
 // half-open interval [l,r)
 std::pair<int, int> subtree(int v) const { return {L[v], R[v]}; }
 // sequence of closed intervals [l,r]
 std::vector<std::pair<int, int>> path(int u, int v, bool edge= 0) const {
  std::vector<std::pair<int, int>> up, down;
  while (PP[u] != PP[v]) {
   if (L[u] < L[v]) down.emplace_back(L[PP[v]], L[v]), v= P[PP[v]];
   else up.emplace_back(L[u], L[PP[u]]), u= P[PP[u]];
  }
  if (L[u] < L[v]) down.emplace_back(L[u] + edge, L[v]);
  else if (L[v] + edge <= L[u]) up.emplace_back(L[u], L[v] + edge);
  return up.insert(up.end(), down.rbegin(), down.rend()), up;
 }
};
#line 4 "src/Graph/Rerooting.hpp"
// put_edge(int v, int e, T t) -> U
// op(U l, U r) -> U
// ui(:U) is the identity element of op
// put_vertex(int v, U sum) -> T
template <class T> class Rerooting {
 HeavyLightDecomposition hld;
 std::valarray<T> dp, dp1, dp2;
public:
 template <class U, class F1, class F2, class F3> Rerooting(const Graph &g, const CSRArray<int> &adje, const HeavyLightDecomposition &hld, const F1 &put_edge, const F2 &op, const U &ui, const F3 &put_vertex) : hld(hld){
  static_assert(std::is_invocable_r_v<U, F1, int, int, T>, "put_edge(int,int,T) is not invocable");
  static_assert(std::is_invocable_r_v<U, F2, U, U>, "op(U,U) is not invocable");
  static_assert(std::is_invocable_r_v<T, F3, int, U>, "put_vertex(int,U) is not invocable");
  const int n= g.vertex_size();
  dp.resize(n), dp1.resize(n), dp2.resize(n);
  for (int i= n, v; i--;) {
   U sum= ui;
   for (int e: adje[v= hld.to_vertex(i)])
    if (int u= g[e].to(v); u != hld.parent(v)) sum= op(sum, put_edge(v, e, dp1[u]));
   dp1[v]= put_vertex(v, sum);
  }
  for (int i= 0, v; i < n; ++i) {
   auto gv= adje[v= hld.to_vertex(i)];
   int dg= gv.size();
   std::valarray<U> f(dg + 1), b(dg + 1);
   for (int j= 0, e, u; j < dg; ++j) u= g[e= gv[j]].to(v), f[j + 1]= put_edge(v, e, u == hld.parent(v) ? dp2[v] : dp1[u]);
   f[0]= b[dg]= ui;
   for (int j= dg; j--;) b[j]= op(f[j + 1], b[j + 1]);
   for (int j= 0; j < dg; ++j) f[j + 1]= op(f[j], f[j + 1]);
   for (int j= 0; j < dg; ++j)
    if (int u= g[gv[j]].to(v); u != hld.parent(v)) dp2[u]= put_vertex(v, op(f[j], b[j + 1]));
   dp[v]= put_vertex(v, f[dg]);
  }
 }
 template <class U, class F1, class F2, class F3> Rerooting(const Graph &g, const CSRArray<int> &adje, const F1 &put_edge, const F2 &op, const U &ui, const F3 &put_vertex): Rerooting(g, adje, HeavyLightDecomposition(g), put_edge, op, ui, put_vertex) {}
 template <class U, class F1, class F2, class F3> Rerooting(const Graph &g, const HeavyLightDecomposition &hld, const F1 &put_edge, const F2 &op, const U &ui, const F3 &put_vertex): Rerooting(g, g.adjacency_edge(0), hld, put_edge, op, ui, put_vertex) {}
 template <class U, class F1, class F2, class F3> Rerooting(const Graph &g, const F1 &put_edge, const F2 &op, const U &ui, const F3 &put_vertex): Rerooting(g, g.adjacency_edge(0), HeavyLightDecomposition(g), put_edge, op, ui, put_vertex) {}
 const T &operator[](int v) const { return dp[v]; }
 auto begin() const { return std::cbegin(dp); }
 auto end() const { return std::cend(dp); }
 const T &operator()(int root, int v) const { return root == v ? dp[v] : hld.in_subtree(root, v) ? dp2[hld.jump(v, root, 1)] : dp1[v]; }
};
#line 2 "src/NumberTheory/Factors.hpp"
#include <numeric>
#line 5 "src/NumberTheory/Factors.hpp"
#include <algorithm>
#line 3 "src/NumberTheory/is_prime.hpp"
namespace math_internal {
template <class Uint, class MP, u32... args> constexpr bool miller_rabin(Uint n) {
 const MP md(n);
 const Uint s= __builtin_ctzll(n - 1), d= n >> s, one= md.set(1), n1= md.norm(md.set(n - 1));
 for (u32 a: (u32[]){args...})
  if (Uint b= a % n; b)
   if (Uint p= md.norm(pow(md.set(b), d, md)); p != one)
    for (int i= s; p != n1; p= md.norm(md.mul(p, p)))
     if (!(--i)) return 0;
 return 1;
}
}
constexpr bool is_prime(unsigned long long n) {
 if (n < 2 || n % 6 % 4 != 1) return (n | 1) == 3;
 if (n < (1 << 30)) return math_internal::miller_rabin<unsigned, math_internal::MP_Mo32, 2, 7, 61>(n);
 if (n < (1ull << 62)) return math_internal::miller_rabin<unsigned long long, math_internal::MP_Mo64, 2, 325, 9375, 28178, 450775, 9780504, 1795265022>(n);
 if (n < (1ull << 63)) return math_internal::miller_rabin<unsigned long long, math_internal::MP_D2B1_1, 2, 325, 9375, 28178, 450775, 9780504, 1795265022>(n);
 return math_internal::miller_rabin<unsigned long long, math_internal::MP_D2B1_2, 2, 325, 9375, 28178, 450775, 9780504, 1795265022>(n);
}
#line 4 "src/Math/binary_gcd.hpp"
#include <cstdint>
template <class Int> constexpr int bsf(Int a) {
 if constexpr (sizeof(Int) == 16) {
  uint64_t lo= a & uint64_t(-1);
  return lo ? __builtin_ctzll(lo) : 64 + __builtin_ctzll(a >> 64);
 } else if constexpr (sizeof(Int) == 8) return __builtin_ctzll(a);
 else return __builtin_ctz(a);
}
template <class Int> constexpr Int binary_gcd(Int a, Int b) {
 if (a == 0 || b == 0) return a + b;
 int n= bsf(a), m= bsf(b), s= 0;
 for (a>>= n, b>>= m; a != b;) {
  Int d= a - b;
  bool f= a > b;
  s= bsf(d), b= f ? b : a, a= (f ? d : -d) >> s;
 }
 return a << std::min(n, m);
}
#line 9 "src/NumberTheory/Factors.hpp"
namespace math_internal {
template <class T> constexpr void bubble_sort(T *bg, T *ed) {
 for (int sz= ed - bg, i= 0; i < sz; i++)
  for (int j= sz; --j > i;)
   if (auto tmp= bg[j - 1]; bg[j - 1] > bg[j]) bg[j - 1]= bg[j], bg[j]= tmp;
}
template <class T, size_t _Nm> struct ConstexprArray {
 constexpr size_t size() const { return sz; }
 constexpr auto &operator[](int i) const { return dat[i]; }
 constexpr auto *begin() const { return dat; }
 constexpr auto *end() const { return dat + sz; }
protected:
 T dat[_Nm]= {};
 size_t sz= 0;
 friend ostream &operator<<(ostream &os, const ConstexprArray &r) {
  os << "[";
  for (size_t i= 0; i < r.sz; ++i) os << r[i] << ",]"[i == r.sz - 1];
  return os;
 }
};
class Factors: public ConstexprArray<pair<u64, uint16_t>, 16> {
 template <class Uint, class MP> static constexpr Uint rho(Uint n, Uint c) {
  const MP md(n);
  auto f= [&md, c](Uint x) { return md.plus(md.mul(x, x), c); };
  const Uint m= 1LL << (__lg(n) / 5);
  Uint x= 1, y= md.set(2), z= 1, q= md.set(1), g= 1;
  for (Uint r= 1, i= 0; g == 1; r<<= 1) {
   for (x= y, i= r; i--;) y= f(y);
   for (Uint k= 0; k < r && g == 1; g= binary_gcd<Uint>(md.get(q), n), k+= m)
    for (z= y, i= min(m, r - k); i--;) y= f(y), q= md.mul(q, md.diff(y, x));
  }
  if (g == n) do {
    z= f(z), g= binary_gcd<Uint>(md.get(md.diff(z, x)), n);
   } while (g == 1);
  return g;
 }
 static constexpr u64 find_prime_factor(u64 n) {
  if (is_prime(n)) return n;
  for (u64 i= 100; i--;)
   if (n= n < (1 << 30) ? rho<u32, MP_Mo32>(n, i + 1) : n < (1ull << 62) ? rho<u64, MP_Mo64>(n, i + 1) : n < (1ull << 62) ? rho<u64, MP_D2B1_1>(n, i + 1) : rho<u64, MP_D2B1_2>(n, i + 1); is_prime(n)) return n;
  return 0;
 }
 constexpr void init(u64 n) {
  for (u64 p= 2; p < 98 && p * p <= n; ++p)
   if (n % p == 0)
    for (dat[sz++].first= p; n % p == 0;) n/= p, ++dat[sz - 1].second;
  for (u64 p= 0; n > 1; dat[sz++].first= p)
   for (p= find_prime_factor(n); n % p == 0;) n/= p, ++dat[sz].second;
 }
public:
 constexpr Factors()= default;
 constexpr Factors(u64 n) { init(n), bubble_sort(dat, dat + sz); }
};
}
using math_internal::Factors;
constexpr uint64_t totient(const Factors &f) {
 uint64_t ret= 1, i= 0;
 for (auto [p, e]: f)
  for (ret*= p - 1, i= e; --i;) ret*= p;
 return ret;
}
constexpr auto totient(uint64_t n) { return totient(Factors(n)); }
template <class Uint= uint64_t> std::vector<Uint> enumerate_divisors(const Factors &f) {
 int k= 1;
 for (auto [p, e]: f) k*= e + 1;
 std::vector<Uint> ret(k, 1);
 k= 1;
 for (auto [p, e]: f) {
  int sz= k;
  for (Uint pw= 1; pw*= p, e--;)
   for (int j= 0; j < sz;) ret[k++]= ret[j++] * pw;
 }
 return ret;
}
template <class Uint> std::vector<Uint> enumerate_divisors(Uint n) { return enumerate_divisors<Uint>(Factors(n)); }
#line 3 "src/NumberTheory/ArrayOnDivisors.hpp"
template <class Int, class T> struct ArrayOnDivisors {
 using Hint= std::conditional_t<sizeof(Int) == 8, unsigned, uint16_t>;
 Int n;
 uint8_t shift;
 std::vector<Hint> os, id;
 std::vector<std::pair<Int, T>> dat;
 Hint hash(uint64_t i) const { return (i * 11995408973635179863ULL) >> shift; }
#define _UP for (int j= k; j < a; ++j)
#define _DWN for (int j= a; j-- > k;)
#define _OP(J, K, op) dat[i + J].second op##= dat[i + K].second
#define _FUN(J, K, name) name(dat[i + J].second, dat[i + K].second)
#define _ZETA(op) \
 int k= 1; \
 for (auto [p, e]: factors) { \
  int a= k * (e + 1); \
  for (int i= 0, d= dat.size(); i < d; i+= a) op; \
  k= a; \
 }
public:
 Factors factors;
 ArrayOnDivisors() {}
 template <class Uint> ArrayOnDivisors(Int N, const Factors &factors, const std::vector<Uint> &divisors): n(N), shift(__builtin_clzll(divisors.size()) - 1), os((1 << (64 - shift)) + 1), id(divisors.size()), dat(divisors.size()), factors(factors) {
  static_assert(std::is_integral_v<Uint>, "Uint must be integral");
  int m= divisors.size(), i= 0;
  for (; i < m; ++i) ++os[hash(dat[i].first= divisors[i])];
  for (std::partial_sum(os.begin(), os.end(), os.begin()); i--;) id[--os[hash(divisors[i])]]= i;
 }
 ArrayOnDivisors(Int N, const Factors &factors): ArrayOnDivisors(N, factors, enumerate_divisors(factors)) {}
 ArrayOnDivisors(Int N): ArrayOnDivisors(N, Factors(N)) {}
 T &operator[](Int i) {
  assert(i && n % i == 0);
  for (unsigned a= hash(i), j= os[a]; j < os[a + 1]; ++j)
   if (auto &[d, v]= dat[id[j]]; d == i) return v;
  assert(0);
 }
 const T &operator[](Int i) const {
  assert(i && n % i == 0);
  for (unsigned a= hash(i), j= os[a]; j < os[a + 1]; ++j)
   if (auto &[d, v]= dat[id[j]]; d == i) return v;
  assert(0);
 }
 size_t size() const { return dat.size(); }
 auto begin() { return dat.begin(); }
 auto begin() const { return dat.begin(); }
 auto end() { return dat.begin() + os.back(); }
 auto end() const { return dat.begin() + os.back(); }
 /* f -> g s.t. g(n) = sum_{m|n} f(m) */
 void divisor_zeta() { _ZETA(_UP _OP(j, j - k, +)) }
 /* f -> h s.t. f(n) = sum_{m|n} h(m) */
 void divisor_mobius() { _ZETA(_DWN _OP(j, j - k, -)) }
 /* f -> g s.t. g(n) = sum_{n|m} f(m) */
 void multiple_zeta() { _ZETA(_DWN _OP(j - k, j, +)) }
 /* f -> h s.t. f(n) = sum_{n|m} h(m) */
 void multiple_mobius() { _ZETA(_UP _OP(j - k, j, -)) }
 /* f -> g s.t. g(n) = sum_{m|n} f(m), add(T& a, T b): a+=b */
 template <class F> void divisor_zeta(const F &add) { _ZETA(_UP _FUN(j, j - k, add)) }
 /* f -> h s.t. f(n) = sum_{m|n} h(m), sub(T& a, T b): a-=b */
 template <class F> void divisor_mobius(const F &sub) { _ZETA(_UP _FUN(j, j - k, sub)) }
 /* f -> g s.t. g(n) = sum_{n|m} f(m), add(T& a, T b): a+=b */
 template <class F> void multiple_zeta(const F &add) { _ZETA(_UP _FUN(j - k, j, add)) }
 /* f -> h s.t. f(n) = sum_{n|m} h(m), sub(T& a, T b): a-=b */
 template <class F> void multiple_mobius(const F &sub) { _ZETA(_UP _FUN(j - k, j, sub)) }
#undef _UP
#undef _DWN
#undef _OP
#undef _ZETA
 // f(p,e): multiplicative function of p^e
 template <typename F> void set_multiplicative(const F &f) {
  int k= 1;
  dat[0].second= 1;
  for (auto [p, e]: factors)
   for (int m= k, d= 1; d <= e; ++d)
    for (int i= 0; i < m;) dat[k++].second= dat[i++].second * f(p, d);
 }
 void set_totient() {
  int k= 1;
  dat[0].second= 1;
  for (auto [p, e]: factors) {
   Int b= p - 1;
   for (int m= k; e--; b*= p)
    for (int i= 0; i < m;) dat[k++].second= dat[i++].second * b;
  }
 }
 void set_mobius() {
  set_multiplicative([](auto, auto e) { return e == 1 ? -1 : 0; });
 }
};
#line 11 "test/atcoder/abc248_g.test.cpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 using Mint= ModInt<998244353>;
 int n;
 cin >> n;
 vector<int> A(n);
 Mint sum= 0;
 for (int &a: A) cin >> a, sum+= a;
 Graph g(n, n - 1);
 for (auto &e: g) cin >> e, --e;
 using T= ArrayOnDivisors<int, pair<int, Mint>>;
 auto put_edge= [&](int v, int, const T &dat) {
  T ret(A[v]);
  for (auto &&[d, a]: dat) {
   auto &[l0, l1]= ret[gcd(d, A[v])];
   auto [r0, r1]= a;
   l1+= r1;
   l0+= r0;
  }
  return ret;
 };
 auto op= [&](const T &l, const T &r) {
  if (l.size() == 0) return r;
  if (r.size() == 0) return l;
  auto ret= l;
  for (auto &[d, a]: ret) {
   auto &[l0, l1]= a;
   auto [r0, r1]= r[d];
   l1+= r1;
   l0+= r0;
  }
  return ret;
 };
 auto put_vertex= [&](int v, T dat) {
  if (dat.size() == 0) dat= T(A[v]);
  dat[A[v]].first+= 1;
  for (auto &[d, x]: dat) x.second+= x.first;
  return dat;
 };
 Mint ans= 0;
 for (auto dat: Rerooting<T>(g, put_edge, op, T(), put_vertex))
  for (auto &&[d, x]: dat) ans+= x.second * d;
 ans-= sum, ans/= 2;
 cout << ans << '\n';
 return 0;
}

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