#include <bits/stdc++.h>
using namespace std;
#define all(...) std::begin(__VA_ARGS__), std::end(__VA_ARGS__)
#define rall(...) std::rbegin(__VA_ARGS__), std::rend(__VA_ARGS__)
#define OVERLOAD_REP(_1, _2, _3, _4, name, ...) name
#define REP1(n) for(ll i=0;i<(n);i++)
#define REP2(i, n) for (ll i=0;i<(n);i++)
#define REP3(i, a, n) for (ll i=a;i<(n);i++)
#define REP4(i, a, b, n) for(ll i=a;i<(n);i+=b)
#define rep(...) OVERLOAD_REP(__VA_ARGS__, REP4, REP3, REP2, REP1)(__VA_ARGS__)
#define OVERLOAD_RREP(_1, _2, _3, _4, name, ...) name
#define RREP1(n) for(ll i=(n)-1;i>=0;i--)
#define RREP2(i, n) for(ll i=(n)-1;i>=0;i--)
#define RREP3(i, a, n) for(ll i=(n)-1;i>=(a);i--)
#define RREP4(i, a, b, n) for(ll i=(n)-1;i>=(a);i-=(b))
#define rrep(...) OVERLOAD_RREP(__VA_ARGS__, RREP4, RREP3, RREP2, RREP1)(__VA_ARGS__)
#define uniq(a) sort(all(a));a.erase(unique(all(a)),end(a))
#define len(n) (long long)(n).size()
using ll = long long;
using ld = long double;
using ull = unsigned long long;
using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vll = vector<ll>;
using vvll = vector<vll>;
using vvvll = vector<vvll>;
using vs = vector<string>;
using vvs = vector<vs>;
using vvvs = vector<vvs>;
using vld = vector<ld>;
using vvld = vector<vld>;
using vvvld = vector<vvld>;
using vc = vector<char>;
using vvc = vector<vc>;
using vvvc = vector<vvc>;
using pll = pair<ll,ll>;
using vpll = vector<pll>;
using vvpll = vector<vpll>;

ll intpow(ll a,ll b){
    ll ans = 1;
    while (b){
        if (b & 1){
            ans *= a;
        }
        a *= a;
        b /= 2;
    }
    return ans;
}
ll modpow(ll a,ll b,ll c){
    ll ans = 1;
    while (b){
        if (b & 1){
            ans *= a;
            ans %= c;
        }
        a *= a;
        a %= c;
        b /= 2;
    }
    return ans;
}

template<class... T>
void input(T&... a){
    (cin >> ... >> a);
}

#define INT(...) int __VA_ARGS__; input(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__; input(__VA_ARGS__)
#define ULL(...) ull __VA_ARGS__; input(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__; input(__VA_ARGS__)
#define STR(...) string __VA_ARGS__; input(__VA_ARGS__)
#define CHA(...) char __VA_ARGS__; input(__VA_ARGS__)
#define VLL(name,length) vll name(length);rep(i,length){cin >> name[i];}
#define VVLL(name,h,w) vvll name(h,vll(w));rep(i,h)rep(j,w){cin >> name[i][j];}
#define VVVLL(name,a,b,c) vvvll name(a,vvll(b,vll(c)));rep(i,a)rep(j,b)rep(k,c){cin >> name[i][j][k];}
#define VI(name,length) vi name(length);rep(i,length){cin >> name[i];}
#define VVI(name,h,w) vvi name(h,vi(w));rep(i,h)rep(j,w){cin >> name[i][j];}
#define VVVI(name,a,b,c) vvvi name(a,vvll(b,vi(c)));rep(i,a)rep(j,b)rep(k,c){cin >> name[i][j][k];}
#define VLD(name,length) vld name(length);rep(i,length){cin >> name[i];}
#define VVLD(name,h,w) vvld name(h,vld(w));rep(i,h)rep(j,w){cin >> name[i][j];}
#define VVVLD(name,a,b,c) vvvld name(a,vvld(b,vld(c)));rep(i,a)rep(j,b)rep(k,c){cin >> name[i][j][k];}
#define VC(name,length) vc name(length);rep(i,length){cin >> name[i];}
#define VVC(name,h,w) vvc name(h,vc(w));rep(i,h)rep(j,w){cin >> name[i][j];}
#define VVVC(name,a,b,c) vvvc name(a,vvc(b,vc(c)));rep(i,a)rep(j,b)rep(k,c){cin >> name[i][j][k];}
#define VS(name,length) vs name(length);rep(i,length){cin >> name[i];}
#define VVS(name,h,w) vvs name(h,vs(w));rep(i,h)rep(j,w){cin >> name[i][j];}
#define VVVS(name,a,b,c) vvvs name(a,vvs(b,vs(c)));rep(i,a)rep(j,b)rep(k,c){cin >> name[i][j][k];}
#define PLL(name) pll name;cin>>name.first>>name.second;
#define VPLL(name,length) vpll name(length);rep(i,length){cin>>name[i].first>>name[i].second;}

void print(){cout << "\n";}

template <typename T1, typename T2>
std::ostream& operator<<(std::ostream& os, const std::pair<T1, T2>& p) {
    os << "(" << p.first << ", " << p.second << ")";
    return os;
}

template <typename T>
std::ostream& operator<<(std::ostream& os, const std::vector<T>& vec) {
    os << "[";
    for (size_t i = 0; i < vec.size(); ++i) {
        os << vec[i];
        if (i + 1 < vec.size()) os << ", ";
    }
    os << "]";
    return os;
}

template <typename T1, typename T2>
std::ostream& operator<<(std::ostream& os, const std::vector<std::pair<T1, T2>>& a) {
    os << "[";
    for (size_t j = 0; j < a.size(); ++j) {
        os << "(" << a[j].first << ", " << a[j].second << ")";
		if (j + 1 < a.size()) os << ", ";
    }
	os << "]";
    return os;
}

template <typename T1, typename T2>
std::ostream& operator<<(std::ostream& os, const std::vector<std::vector<std::pair<T1, T2>>>& mat) {
	os << "[";
    for (size_t i = 0; i < mat.size(); ++i) {
		os << "[";
        for (size_t j = 0; j < mat[i].size(); ++j) {
            os << "(" << mat[i][j].first << ", " << mat[i][j].second << ")";
			if (j + 1 < mat[i].size()) os << ", ";
        }
		os << "]";
		if (i + 1 < mat.size()) os << ", ";
    }
	os << "]";
    return os;
}

template <typename T>
std::ostream& operator<<(std::ostream& os, const std::set<T>& s) {
    os << "{";
    bool first = true;
    for (const auto& x : s) {
        if (!first) os << ", ";
        os << x;
        first = false;
    }
    os << "}";
    return os;
}

template <typename K, typename V>
std::ostream& operator<<(std::ostream& os, const std::map<K, V>& m) {
    os << "{";
    bool first = true;
    for (const auto& [key, val] : m) {
        if (!first) os << ", ";
        os << key << ": " << val;
        first = false;
    }
    os << "}";
    return os;
}

template<class T, class... Ts>
void print(const T& a, const Ts&... b){cout << a;(cout << ... << (cout << ' ', b));cout << '\n';}

#ifdef LOCAL
void debug() { std::cerr << "\n"; }

template<class T, class... Ts>
void debug(const T& a, const Ts&... b) {
    std::cerr << a;
    (std::cerr << ... << (std::cerr << ' ', b));
    std::cerr << '\n';
}
#else
#define debug(...) (void)0
#endif

void write(){cout << "\n";}
template<class T, class... Ts>
void write(const T& a, const Ts&... b){cout << a;(cout << ... << (cout << ' ', b));cout << '\n';}
void write(vll x){rep(i,len(x)){cout << x[i];if(i!=len(x)-1){cout << " ";}else{cout << '\n';}}}
void write(vvll x){rep(i,len(x))rep(j,len(x[i])){cout << x[i][j];if(j!=len(x[i])-1){cout << " ";}else{cout << '\n';}}}
void write(vi x){rep(i,len(x)){cout << x[i];if(i!=len(x)-1){cout << " ";}else{cout << '\n';}}}
void write(vvi x){rep(i,len(x))rep(j,len(x[i])){cout << x[i][j];if(j!=len(x[i])-1){cout << " ";}else{cout << '\n';}}}
void write(vvvi x){rep(i,len(x))rep(j,len(x[i]))rep(k,len(x[i][j])){cout << x[i][j][k];if(k!=len(x[i][j])-1){cout << " ";}else if(j!=len(x[i])-1){cout << " | ";}else{cout << '\n';}}}
void write(vld x){rep(i,len(x)){cout << x[i];if(i!=len(x)-1){cout << " ";}else{cout << '\n';}}}
void write(vvld x){rep(i,len(x))rep(j,len(x[i])){cout << x[i][j];if(j!=len(x[i])-1){cout << " ";}else{cout << '\n';}}}
void write(vvvld x){rep(i,len(x))rep(j,len(x[i]))rep(k,len(x[i][j])){cout << x[i][j][k];if(k!=len(x[i][j])-1){cout << " ";}else if(j!=len(x[i])-1){cout << " | ";}else{cout << '\n';}}}
void write(vc x){rep(i,len(x)){cout << x[i];if(i!=len(x)-1){cout << " ";}else{cout << '\n';}}}
void write(vvc x){rep(i,len(x))rep(j,len(x[i])){cout << x[i][j];if(j!=len(x[i])-1){cout << " ";}else{cout << '\n';}}}
void write(vvvc x){rep(i,len(x))rep(j,len(x[i]))rep(k,len(x[i][j])){cout << x[i][j][k];if(k!=len(x[i][j])-1){cout << " ";}else if(j!=len(x[i])-1){cout << " | ";}else{cout << '\n';}}}
void write(vs x){rep(i,len(x)){cout << x[i];if(i!=len(x)-1){cout << " ";}else{cout << '\n';}}}
void write(vvs x){rep(i,len(x))rep(j,len(x[i])){cout << x[i][j];if(j!=len(x[i])-1){cout << " ";}else{cout << '\n';}}}
void write(vvvs x){rep(i,len(x))rep(j,len(x[i]))rep(k,len(x[i][j])){cout << x[i][j][k];if(k!=len(x[i][j])-1){cout << " ";}else if(j!=len(x[i])-1){cout << " | ";}else{cout << '\n';}}}
void write(pll x){cout << x.first << ' ' << x.second << '\n';}
void write(vpll x){rep(i,len(x)){cout << x[i].first << ' ' << x[i].second << '\n';}}
void write(vvpll x){rep(i,len(x))rep(j,len(x[i])){cout << x[i][j].first << ' ' << x[i][j].second;if(j!=len(x[i])-1){cout << " ";}else{cout << '\n';}}}

template <typename T>
T sum(const std::vector<T>& v) {
    return std::accumulate(v.begin(), v.end(), T(0));
}

template<class T> bool chmin(T& a, const T& b){ if(a > b){ a = b; return 1; } return 0; }
template<class T> bool chmax(T& a, const T& b){ if(a < b){ a = b; return 1; } return 0; }
template<class T, class U> bool chmin(T& a, const U& b){ if(a > T(b)){ a = b; return 1; } return 0; }
template<class T, class U> bool chmax(T& a, const U& b){ if(a < T(b)){ a = b; return 1; } return 0; }

#include <atcoder/modint>
using mint = atcoder::modint998244353;
using vm = vector<mint>;
#line 2 "prime/fast-factorize.hpp"

#include <cstdint>
#include <numeric>
#include <vector>
using namespace std;

#line 2 "internal/internal-math.hpp"

#line 2 "internal/internal-type-traits.hpp"

#include <type_traits>
using namespace std;

namespace internal {
template <typename T>
using is_broadly_integral =
    typename conditional_t<is_integral_v<T> || is_same_v<T, __int128_t> ||
                               is_same_v<T, __uint128_t>,
                           true_type, false_type>::type;

template <typename T>
using is_broadly_signed =
    typename conditional_t<is_signed_v<T> || is_same_v<T, __int128_t>,
                           true_type, false_type>::type;

template <typename T>
using is_broadly_unsigned =
    typename conditional_t<is_unsigned_v<T> || is_same_v<T, __uint128_t>,
                           true_type, false_type>::type;

#define ENABLE_VALUE(x) \
  template <typename T> \
  constexpr bool x##_v = x<T>::value;

ENABLE_VALUE(is_broadly_integral);
ENABLE_VALUE(is_broadly_signed);
ENABLE_VALUE(is_broadly_unsigned);
#undef ENABLE_VALUE

#define ENABLE_HAS_TYPE(var)                                   \
  template <class, class = void>                               \
  struct has_##var : false_type {};                            \
  template <class T>                                           \
  struct has_##var<T, void_t<typename T::var>> : true_type {}; \
  template <class T>                                           \
  constexpr auto has_##var##_v = has_##var<T>::value;

#define ENABLE_HAS_VAR(var)                                     \
  template <class, class = void>                                \
  struct has_##var : false_type {};                             \
  template <class T>                                            \
  struct has_##var<T, void_t<decltype(T::var)>> : true_type {}; \
  template <class T>                                            \
  constexpr auto has_##var##_v = has_##var<T>::value;

}  // namespace internal
#line 4 "internal/internal-math.hpp"

namespace internal {

#include <cassert>
#include <utility>
#line 10 "internal/internal-math.hpp"
using namespace std;

// a mod p
template <typename T>
T safe_mod(T a, T p) {
  a %= p;
  if constexpr (is_broadly_signed_v<T>) {
    if (a < 0) a += p;
  }
  return a;
}

// 返り値：pair(g, x)
// s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
template <typename T>
pair<T, T> inv_gcd(T a, T p) {
  static_assert(is_broadly_signed_v<T>);
  a = safe_mod(a, p);
  if (a == 0) return {p, 0};
  T b = p, x = 1, y = 0;
  while (a != 0) {
    T q = b / a;
    swap(a, b %= a);
    swap(x, y -= q * x);
  }
  if (y < 0) y += p / b;
  return {b, y};
}

// 返り値 : a^{-1} mod p
// gcd(a, p) != 1 が必要
template <typename T>
T inv(T a, T p) {
  static_assert(is_broadly_signed_v<T>);
  a = safe_mod(a, p);
  T b = p, x = 1, y = 0;
  while (a != 0) {
    T q = b / a;
    swap(a, b %= a);
    swap(x, y -= q * x);
  }
  assert(b == 1);
  return y < 0 ? y + p : y;
}

// T : 底の型
// U : T*T がオーバーフローしない かつ 指数の型
template <typename T, typename U>
T modpow(T a, U n, T p) {
  a = safe_mod(a, p);
  T ret = 1 % p;
  while (n != 0) {
    if (n % 2 == 1) ret = U(ret) * a % p;
    a = U(a) * a % p;
    n /= 2;
  }
  return ret;
}

// 返り値 : pair(rem, mod)
// 解なしのときは {0, 0} を返す
template <typename T>
pair<T, T> crt(const vector<T>& r, const vector<T>& m) {
  static_assert(is_broadly_signed_v<T>);
  assert(r.size() == m.size());
  int n = int(r.size());
  T r0 = 0, m0 = 1;
  for (int i = 0; i < n; i++) {
    assert(1 <= m[i]);
    T r1 = safe_mod(r[i], m[i]), m1 = m[i];
    if (m0 < m1) swap(r0, r1), swap(m0, m1);
    if (m0 % m1 == 0) {
      if (r0 % m1 != r1) return {0, 0};
      continue;
    }
    auto [g, im] = inv_gcd(m0, m1);
    T u1 = m1 / g;
    if ((r1 - r0) % g) return {0, 0};
    T x = (r1 - r0) / g % u1 * im % u1;
    r0 += x * m0;
    m0 *= u1;
    if (r0 < 0) r0 += m0;
  }
  return {r0, m0};
}

}  // namespace internal
#line 2 "misc/rng.hpp"

#line 2 "internal/internal-seed.hpp"

#include <chrono>
using namespace std;

namespace internal {
unsigned long long non_deterministic_seed() {
  unsigned long long m =
      chrono::duration_cast<chrono::nanoseconds>(
          chrono::high_resolution_clock::now().time_since_epoch())
          .count();
  m ^= 9845834732710364265uLL;
  m ^= m << 24, m ^= m >> 31, m ^= m << 35;
  return m;
}
unsigned long long deterministic_seed() { return 88172645463325252UL; }

// 64 bit の seed 値を生成 (手元では seed 固定)
// 連続で呼び出すと同じ値が何度も返ってくるので注意
// #define RANDOMIZED_SEED するとシードがランダムになる
unsigned long long seed() {
#if defined(NyaanLocal) && !defined(RANDOMIZED_SEED)
  return deterministic_seed();
#else
  return non_deterministic_seed();
#endif
}

}  // namespace internal
#line 4 "misc/rng.hpp"

namespace my_rand {
using i64 = long long;
using u64 = unsigned long long;

// [0, 2^64 - 1)
u64 rng() {
  static u64 _x = internal::seed();
  return _x ^= _x << 7, _x ^= _x >> 9;
}

// [l, r]
i64 rng(i64 l, i64 r) {
  assert(l <= r);
  return l + rng() % u64(r - l + 1);
}

// [l, r)
i64 randint(i64 l, i64 r) {
  assert(l < r);
  return l + rng() % u64(r - l);
}

// choose n numbers from [l, r) without overlapping
vector<i64> randset(i64 l, i64 r, i64 n) {
  assert(l <= r && n <= r - l);
  unordered_set<i64> s;
  for (i64 i = n; i; --i) {
    i64 m = randint(l, r + 1 - i);
    if (s.find(m) != s.end()) m = r - i;
    s.insert(m);
  }
  vector<i64> ret;
  for (auto& x : s) ret.push_back(x);
  sort(begin(ret), end(ret));
  return ret;
}

// [0.0, 1.0)
double rnd() { return rng() * 5.42101086242752217004e-20; }
// [l, r)
double rnd(double l, double r) {
  assert(l < r);
  return l + rnd() * (r - l);
}

template <typename T>
void randshf(vector<T>& v) {
  int n = v.size();
  for (int i = 1; i < n; i++) swap(v[i], v[randint(0, i + 1)]);
}

}  // namespace my_rand

using my_rand::randint;
using my_rand::randset;
using my_rand::randshf;
using my_rand::rnd;
using my_rand::rng;
#line 2 "modint/arbitrary-montgomery-modint.hpp"

#include <iostream>
using namespace std;

template <typename Int, typename UInt, typename Long, typename ULong, int id>
struct ArbitraryLazyMontgomeryModIntBase {
  using mint = ArbitraryLazyMontgomeryModIntBase;

  inline static UInt mod;
  inline static UInt r;
  inline static UInt n2;
  static constexpr int bit_length = sizeof(UInt) * 8;

  static UInt get_r() {
    UInt ret = mod;
    while (mod * ret != 1) ret *= UInt(2) - mod * ret;
    return ret;
  }
  static void set_mod(UInt m) {
    assert(m < (UInt(1u) << (bit_length - 2)));
    assert((m & 1) == 1);
    mod = m, n2 = -ULong(m) % m, r = get_r();
  }
  UInt a;

  ArbitraryLazyMontgomeryModIntBase() : a(0) {}
  ArbitraryLazyMontgomeryModIntBase(const Long &b)
      : a(reduce(ULong(b % mod + mod) * n2)){};

  static UInt reduce(const ULong &b) {
    return (b + ULong(UInt(b) * UInt(-r)) * mod) >> bit_length;
  }

  mint &operator+=(const mint &b) {
    if (Int(a += b.a - 2 * mod) < 0) a += 2 * mod;
    return *this;
  }
  mint &operator-=(const mint &b) {
    if (Int(a -= b.a) < 0) a += 2 * mod;
    return *this;
  }
  mint &operator*=(const mint &b) {
    a = reduce(ULong(a) * b.a);
    return *this;
  }
  mint &operator/=(const mint &b) {
    *this *= b.inverse();
    return *this;
  }

  mint operator+(const mint &b) const { return mint(*this) += b; }
  mint operator-(const mint &b) const { return mint(*this) -= b; }
  mint operator*(const mint &b) const { return mint(*this) *= b; }
  mint operator/(const mint &b) const { return mint(*this) /= b; }

  bool operator==(const mint &b) const {
    return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
  }
  bool operator!=(const mint &b) const {
    return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
  }
  mint operator-() const { return mint(0) - mint(*this); }
  mint operator+() const { return mint(*this); }

  mint pow(ULong n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul, n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const mint &b) {
    return os << b.get();
  }

  friend istream &operator>>(istream &is, mint &b) {
    Long t;
    is >> t;
    b = ArbitraryLazyMontgomeryModIntBase(t);
    return (is);
  }

  mint inverse() const {
    Int x = get(), y = get_mod(), u = 1, v = 0;
    while (y > 0) {
      Int t = x / y;
      swap(x -= t * y, y);
      swap(u -= t * v, v);
    }
    return mint{u};
  }

  UInt get() const {
    UInt ret = reduce(a);
    return ret >= mod ? ret - mod : ret;
  }

  static UInt get_mod() { return mod; }
};

// id に適当な乱数を割り当てて使う
template <int id>
using ArbitraryLazyMontgomeryModInt =
    ArbitraryLazyMontgomeryModIntBase<int, unsigned int, long long,
                                      unsigned long long, id>;
template <int id>
using ArbitraryLazyMontgomeryModInt64bit =
    ArbitraryLazyMontgomeryModIntBase<long long, unsigned long long, __int128_t,
                                      __uint128_t, id>;
#line 2 "prime/miller-rabin.hpp"

#line 4 "prime/miller-rabin.hpp"
using namespace std;

#line 8 "prime/miller-rabin.hpp"

namespace fast_factorize {

template <typename T, typename U>
bool miller_rabin(const T& n, vector<T> ws) {
  if (n <= 2) return n == 2;
  if (n % 2 == 0) return false;

  T d = n - 1;
  while (d % 2 == 0) d /= 2;
  U e = 1, rev = n - 1;
  for (T w : ws) {
    if (w % n == 0) continue;
    T t = d;
    U y = internal::modpow<T, U>(w, t, n);
    while (t != n - 1 && y != e && y != rev) y = y * y % n, t *= 2;
    if (y != rev && t % 2 == 0) return false;
  }
  return true;
}

bool miller_rabin_u64(unsigned long long n) {
  return miller_rabin<unsigned long long, __uint128_t>(
      n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});
}

template <typename mint>
bool miller_rabin(unsigned long long n, vector<unsigned long long> ws) {
  if (n <= 2) return n == 2;
  if (n % 2 == 0) return false;

  if (mint::get_mod() != n) mint::set_mod(n);
  unsigned long long d = n - 1;
  while (~d & 1) d >>= 1;
  mint e = 1, rev = n - 1;
  for (unsigned long long w : ws) {
    if (w % n == 0) continue;
    unsigned long long t = d;
    mint y = mint(w).pow(t);
    while (t != n - 1 && y != e && y != rev) y *= y, t *= 2;
    if (y != rev && t % 2 == 0) return false;
  }
  return true;
}

bool is_prime(unsigned long long n) {
  using mint32 = ArbitraryLazyMontgomeryModInt<96229631>;
  using mint64 = ArbitraryLazyMontgomeryModInt64bit<622196072>;

  if (n <= 2) return n == 2;
  if (n % 2 == 0) return false;
  if (n < (1uLL << 30)) {
    return miller_rabin<mint32>(n, {2, 7, 61});
  } else if (n < (1uLL << 62)) {
    return miller_rabin<mint64>(
        n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});
  } else {
    return miller_rabin_u64(n);
  }
}

}  // namespace fast_factorize

using fast_factorize::is_prime;

/**
 * @brief Miller-Rabin primality test
 */
#line 12 "prime/fast-factorize.hpp"

namespace fast_factorize {
using u64 = uint64_t;

template <typename mint, typename T>
T pollard_rho(T n) {
  if (~n & 1) return 2;
  if (is_prime(n)) return n;
  if (mint::get_mod() != n) mint::set_mod(n);
  mint R, one = 1;
  auto f = [&](mint x) { return x * x + R; };
  auto rnd_ = [&]() { return rng() % (n - 2) + 2; };
  while (1) {
    mint x, y, ys, q = one;
    R = rnd_(), y = rnd_();
    T g = 1;
    constexpr int m = 128;
    for (int r = 1; g == 1; r <<= 1) {
      x = y;
      for (int i = 0; i < r; ++i) y = f(y);
      for (int k = 0; g == 1 && k < r; k += m) {
        ys = y;
        for (int i = 0; i < m && i < r - k; ++i) q *= x - (y = f(y));
        g = gcd(q.get(), n);
      }
    }
    if (g == n) do
        g = gcd((x - (ys = f(ys))).get(), n);
      while (g == 1);
    if (g != n) return g;
  }
  exit(1);
}

using i64 = long long;

vector<i64> inner_factorize(u64 n) {
  using mint32 = ArbitraryLazyMontgomeryModInt<452288976>;
  using mint64 = ArbitraryLazyMontgomeryModInt64bit<401243123>;

  if (n <= 1) return {};
  u64 p;
  if (n <= (1LL << 30)) {
    p = pollard_rho<mint32, uint32_t>(n);
  } else if (n <= (1LL << 62)) {
    p = pollard_rho<mint64, uint64_t>(n);
  } else {
    exit(1);
  }
  if (p == n) return {i64(p)};
  auto l = inner_factorize(p);
  auto r = inner_factorize(n / p);
  copy(begin(r), end(r), back_inserter(l));
  return l;
}

vector<i64> factorize(u64 n) {
  auto ret = inner_factorize(n);
  sort(begin(ret), end(ret));
  return ret;
}

map<i64, i64> factor_count(u64 n) {
  map<i64, i64> mp;
  for (auto &x : factorize(n)) mp[x]++;
  return mp;
}

vector<i64> divisors(u64 n) {
  if (n == 0) return {};
  vector<pair<i64, i64>> v;
  for (auto &p : factorize(n)) {
    if (v.empty() || v.back().first != p) {
      v.emplace_back(p, 1);
    } else {
      v.back().second++;
    }
  }
  vector<i64> ret;
  auto f = [&](auto rc, int i, i64 x) -> void {
    if (i == (int)v.size()) {
      ret.push_back(x);
      return;
    }
    rc(rc, i + 1, x);
    for (int j = 0; j < v[i].second; j++) rc(rc, i + 1, x *= v[i].first);
  };
  f(f, 0, 1);
  sort(begin(ret), end(ret));
  return ret;
}

}  // namespace fast_factorize

using fast_factorize::divisors;
using fast_factorize::factor_count;
using fast_factorize::factorize;

/**
 * @brief 高速素因数分解(Miller Rabin/Pollard's Rho)
 * @docs docs/prime/fast-factorize.md
 */

int main(){
	ios::sync_with_stdio(false);
	std::cin.tie(nullptr);

    LL(n);
    VLL(a,n);
    vvll edge(n);
    rep(i,n-1){
        LL(u,v);
        u--;
        v--;
        edge[u].push_back(v);
        edge[v].push_back(u);
    }
    vector<map<ll,ll>> mp(n);
    vm dp(n,1);
    vector<map<ll,ll>> fact(n);
    rep(i,n){
        fact[i] = factor_count(a[i]);
    }
    vm inv(1000000+10);
    rep(i,1,1000000+10){
        inv[i] = mint(i).inv();
    }
    auto dfs = [&](auto dfs,ll now,ll p) -> void {
        dp[now] = mint(a[now]);
        map<ll,ll> temp = fact[now];
        for(auto to:edge[now]){
            if(to == p){continue;}
            dfs(dfs,to,now);
            for(auto [k,v]:mp[to]){
                ll l = max(0LL,v - temp[k]);
                dp[now] *= mint(k).pow(l);
                chmax(temp[k],v);
            }
        }
        mp[now] = temp;
    };
    dfs(dfs,0,-1);
    rep(i,n){
        print(dp[i].val());
    }

}