#line 2 "convolution/ntt.hpp"

#include <algorithm>
#include <array>
#include <bit>
#include <cassert>
#include <vector>

#line 2 "math/internal_math.hpp"

#line 4 "math/internal_math.hpp"

namespace ebi {

namespace internal {

constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    if (m == 880803841) return 26;
    if (m == 924844033) return 5;
    return -1;
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);

}  // namespace internal

}  // namespace ebi
#line 2 "modint/base.hpp"

#include <concepts>
#include <iostream>
#include <utility>

namespace ebi {

template <class T>
concept Modint = requires(T a, T b) {
    a + b;
    a - b;
    a * b;
    a / b;
    a.inv();
    a.val();
    a.pow(std::declval<long long>());
    T::mod();
};

template <Modint mint> std::istream &operator>>(std::istream &os, mint &a) {
    long long x;
    os >> x;
    a = x;
    return os;
}

template <Modint mint>
std::ostream &operator<<(std::ostream &os, const mint &a) {
    return os << a.val();
}

}  // namespace ebi
#line 11 "convolution/ntt.hpp"

namespace ebi {

namespace internal {

template <Modint mint, int g = internal::primitive_root<mint::mod()>>
struct ntt_info {
    static constexpr int rank2 =
        std::countr_zero((unsigned int)(mint::mod() - 1));

    std::array<mint, rank2 + 1> root, inv_root;

    ntt_info() {
        root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
        inv_root[rank2] = root[rank2].inv();
        for (int i = rank2 - 1; i >= 0; i--) {
            root[i] = root[i + 1] * root[i + 1];
            inv_root[i] = inv_root[i + 1] * inv_root[i + 1];
        }
    }
};

template <Modint mint> void butterfly(std::vector<mint>& a) {
    static const ntt_info<mint> info;
    int n = int(a.size());
    int bit_size = std::countr_zero(a.size());
    assert(n == (int)std::bit_ceil(a.size()));

    // bit reverse
    for (int i = 0, j = 1; j < n - 1; j++) {
        for (int k = n >> 1; k > (i ^= k); k >>= 1)
            ;
        if (j < i) {
            std::swap(a[i], a[j]);
        }
    }

    for (int bit = 0; bit < bit_size; bit++) {
        for (int i = 0; i < n / (1 << (bit + 1)); i++) {
            mint zeta1 = 1;
            mint zeta2 = info.root[1];
            for (int j = 0; j < (1 << bit); j++) {
                int idx = i * (1 << (bit + 1)) + j;
                int jdx = idx + (1 << bit);
                mint p1 = a[idx];
                mint p2 = a[jdx];
                a[idx] = p1 + zeta1 * p2;
                a[jdx] = p1 + zeta2 * p2;
                zeta1 *= info.root[bit + 1];
                zeta2 *= info.root[bit + 1];
            }
        }
    }
}

template <Modint mint> void butterfly_inv(std::vector<mint>& a) {
    static const ntt_info<mint> info;
    int n = int(a.size());
    int bit_size = std::countr_zero(a.size());
    assert(n == (int)std::bit_ceil(a.size()));

    // bit reverse
    for (int i = 0, j = 1; j < n - 1; j++) {
        for (int k = n >> 1; k > (i ^= k); k >>= 1)
            ;
        if (j < i) {
            std::swap(a[i], a[j]);
        }
    }

    for (int bit = 0; bit < bit_size; bit++) {
        for (int i = 0; i < n / (1 << (bit + 1)); i++) {
            mint zeta1 = 1;
            mint zeta2 = info.inv_root[1];
            for (int j = 0; j < (1 << bit); j++) {
                int idx = i * (1 << (bit + 1)) + j;
                int jdx = idx + (1 << bit);
                mint p1 = a[idx];
                mint p2 = a[jdx];
                a[idx] = p1 + zeta1 * p2;
                a[jdx] = p1 + zeta2 * p2;
                zeta1 *= info.inv_root[bit + 1];
                zeta2 *= info.inv_root[bit + 1];
            }
        }
    }
    mint inv_n = mint(n).inv();
    for (int i = 0; i < n; i++) {
        a[i] *= inv_n;
    }
}

}  // namespace internal

template <Modint mint>
std::vector<mint> convolution_naive(const std::vector<mint>& f,
                                    const std::vector<mint>& g) {
    if (f.empty() || g.empty()) return {};
    int n = int(f.size()), m = int(g.size());
    std::vector<mint> c(n + m - 1);
    if (n < m) {
        for (int j = 0; j < m; j++) {
            for (int i = 0; i < n; i++) {
                c[i + j] += f[i] * g[j];
            }
        }
    } else {
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                c[i + j] += f[i] * g[j];
            }
        }
    }
    return c;
}

template <Modint mint>
std::vector<mint> convolution(const std::vector<mint>& f,
                              const std::vector<mint>& g) {
    if (f.empty() || g.empty()) return {};
    if (std::min(f.size(), g.size()) < 60) return convolution_naive(f, g);
    int n = std::bit_ceil(f.size() + g.size() - 1);
    std::vector<mint> a(n), b(n);
    std::copy(f.begin(), f.end(), a.begin());
    std::copy(g.begin(), g.end(), b.begin());
    internal::butterfly(a);
    internal::butterfly(b);
    for (int i = 0; i < n; i++) {
        a[i] *= b[i];
    }
    internal::butterfly_inv(a);
    a.resize(f.size() + g.size() - 1);
    return a;
}

}  // namespace ebi
#line 2 "fps/middle_product.hpp"

#line 7 "fps/middle_product.hpp"

#line 9 "fps/middle_product.hpp"

namespace ebi {

template <Modint mint,
          std::vector<mint> (*convolution)(const std::vector<mint> &,
                                           const std::vector<mint> &)>
std::vector<mint> middle_product(const std::vector<mint> &a,
                                const std::vector<mint> &b) {
    assert(a.size() >= b.size());
    auto rb = b;
    std::reverse(rb.begin(), rb.end());
    std::vector<mint> c = convolution(a, rb);
    c.resize(a.size());
    c.erase(c.begin(), c.begin() + b.size() - 1);
    return c;
}

}  // namespace ebi
#line 2 "graph/template.hpp"

#line 4 "graph/template.hpp"

namespace ebi {

template <class T> struct Edge {
    int to;
    T cost;
    Edge(int _to, T _cost = 1) : to(_to), cost(_cost) {}
};

template <class T> struct Graph : std::vector<std::vector<Edge<T>>> {
    using std::vector<std::vector<Edge<T>>>::vector;
    void add_edge(int u, int v, T w, bool directed = false) {
        (*this)[u].emplace_back(v, w);
        if (directed) return;
        (*this)[v].emplace_back(u, w);
    }
};

struct graph : std::vector<std::vector<int>> {
    using std::vector<std::vector<int>>::vector;
    void add_edge(int u, int v, bool directed = false) {
        (*this)[u].emplace_back(v);
        if (directed) return;
        (*this)[v].emplace_back(u);
    }
};

}  // namespace ebi
#line 2 "modint/modint.hpp"

#line 5 "modint/modint.hpp"

#line 7 "modint/modint.hpp"

namespace ebi {

template <int m> struct static_modint {
  private:
    using modint = static_modint;

  public:
    static constexpr int mod() {
        return m;
    }

    static constexpr modint raw(int v) {
        modint x;
        x._v = v;
        return x;
    }

    constexpr static_modint() : _v(0) {}

    constexpr static_modint(long long v) {
        v %= (long long)umod();
        if (v < 0) v += (long long)umod();
        _v = (unsigned int)v;
    }

    constexpr unsigned int val() const {
        return _v;
    }

    constexpr unsigned int value() const {
        return val();
    }

    constexpr modint &operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    constexpr modint &operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }

    constexpr modint operator++(int) {
        modint res = *this;
        ++*this;
        return res;
    }
    constexpr modint operator--(int) {
        modint res = *this;
        --*this;
        return res;
    }

    constexpr modint &operator+=(const modint &rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    constexpr modint &operator-=(const modint &rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    constexpr modint &operator*=(const modint &rhs) {
        unsigned long long x = _v;
        x *= rhs._v;
        _v = (unsigned int)(x % (unsigned long long)umod());
        return *this;
    }
    constexpr modint &operator/=(const modint &rhs) {
        return *this = *this * rhs.inv();
    }

    constexpr modint operator+() const {
        return *this;
    }
    constexpr modint operator-() const {
        return modint() - *this;
    }

    constexpr modint pow(long long n) const {
        assert(0 <= n);
        modint x = *this, res = 1;
        while (n) {
            if (n & 1) res *= x;
            x *= x;
            n >>= 1;
        }
        return res;
    }
    constexpr modint inv() const {
        assert(_v);
        return pow(umod() - 2);
    }

    friend modint operator+(const modint &lhs, const modint &rhs) {
        return modint(lhs) += rhs;
    }
    friend modint operator-(const modint &lhs, const modint &rhs) {
        return modint(lhs) -= rhs;
    }
    friend modint operator*(const modint &lhs, const modint &rhs) {
        return modint(lhs) *= rhs;
    }

    friend modint operator/(const modint &lhs, const modint &rhs) {
        return modint(lhs) /= rhs;
    }
    friend bool operator==(const modint &lhs, const modint &rhs) {
        return lhs.val() == rhs.val();
    }
    friend bool operator!=(const modint &lhs, const modint &rhs) {
        return !(lhs == rhs);
    }

  private:
    unsigned int _v = 0;

    static constexpr unsigned int umod() {
        return m;
    }
};

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;

}  // namespace ebi
#line 3 "template/template.hpp"
#include <bitset>
#line 5 "template/template.hpp"
#include <chrono>
#include <climits>
#include <cmath>
#include <complex>
#include <cstddef>
#include <cstdint>
#include <cstdlib>
#include <cstring>
#include <functional>
#include <iomanip>
#line 16 "template/template.hpp"
#include <limits>
#include <map>
#include <memory>
#include <numbers>
#include <numeric>
#include <optional>
#include <queue>
#include <random>
#include <ranges>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#line 34 "template/template.hpp"

#define rep(i, a, n) for (int i = (int)(a); i < (int)(n); i++)
#define rrep(i, a, n) for (int i = ((int)(n)-1); i >= (int)(a); i--)
#define Rep(i, a, n) for (i64 i = (i64)(a); i < (i64)(n); i++)
#define RRep(i, a, n) for (i64 i = ((i64)(n)-i64(1)); i >= (i64)(a); i--)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()

#line 2 "template/debug_template.hpp"

#line 4 "template/debug_template.hpp"

namespace ebi {

#ifdef LOCAL
#define debug(...)                                                      \
    std::cerr << "LINE: " << __LINE__ << "  [" << #__VA_ARGS__ << "]:", \
        debug_out(__VA_ARGS__)
#else
#define debug(...)
#endif

void debug_out() {
    std::cerr << std::endl;
}

template <typename Head, typename... Tail> void debug_out(Head h, Tail... t) {
    std::cerr << " " << h;
    if (sizeof...(t) > 0) std::cerr << " :";
    debug_out(t...);
}

}  // namespace ebi
#line 2 "template/int_alias.hpp"

#line 4 "template/int_alias.hpp"

namespace ebi {

using ld = long double;
using std::size_t;
using i8 = std::int8_t;
using u8 = std::uint8_t;
using i16 = std::int16_t;
using u16 = std::uint16_t;
using i32 = std::int32_t;
using u32 = std::uint32_t;
using i64 = std::int64_t;
using u64 = std::uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;

}  // namespace ebi
#line 2 "template/io.hpp"

#line 7 "template/io.hpp"

namespace ebi {

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

template <typename T1, typename T2>
std::istream &operator>>(std::istream &os, std::pair<T1, T2> &pa) {
    return os >> pa.first >> pa.second;
}

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

template <typename T>
std::istream &operator>>(std::istream &os, std::vector<T> &vec) {
    for (T &e : vec) std::cin >> e;
    return os;
}

template <typename T>
std::ostream &operator<<(std::ostream &os, const std::optional<T> &opt) {
    if (opt) {
        os << opt.value();
    } else {
        os << "invalid value";
    }
    return os;
}

void fast_io() {
    std::cout << std::fixed << std::setprecision(15);
    std::cin.tie(nullptr);
    std::ios::sync_with_stdio(false);
}

}  // namespace ebi
#line 2 "template/utility.hpp"

#line 5 "template/utility.hpp"

#line 7 "template/utility.hpp"

namespace ebi {

template <class T> inline bool chmin(T &a, T b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}

template <class T> inline bool chmax(T &a, T b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

template <class T> T safe_ceil(T a, T b) {
    if (a % b == 0)
        return a / b;
    else if (a >= 0)
        return (a / b) + 1;
    else
        return -((-a) / b);
}

template <class T> T safe_floor(T a, T b) {
    if (a % b == 0)
        return a / b;
    else if (a >= 0)
        return a / b;
    else
        return -((-a) / b) - 1;
}

constexpr i64 LNF = std::numeric_limits<i64>::max() / 4;

constexpr int INF = std::numeric_limits<int>::max() / 2;

const std::vector<int> dy = {1, 0, -1, 0, 1, 1, -1, -1};
const std::vector<int> dx = {0, 1, 0, -1, 1, -1, 1, -1};

}  // namespace ebi
#line 2 "tree/centroid_decomposition.hpp"

#line 7 "tree/centroid_decomposition.hpp"

namespace ebi {

namespace internal {

template <class F>
void centroid_decomposition_dfs_naive(const std::vector<int> &par,
                                      const std::vector<int> &original_vs,
                                      F f) {
    const int n = (int)par.size();
    assert(par.size() == original_vs.size());
    int center = -1;
    std::vector<int> sz(n, 1);
    for (const int v : std::views::iota(0, n) | std::views::reverse) {
        if (sz[v] >= (n + 1) / 2) {
            center = v;
            break;
        }
        sz[par[v]] += sz[v];
    }
    std::vector<int> color(n, -1);
    std::vector<int> vs = {center};
    color[center] = 0;
    int c = 1;
    for (const int v : std::views::iota(1, n)) {
        if (par[v] == center) {
            vs.emplace_back(v);
            color[v] = c++;
        }
    }
    if (center > 0) {
        for (int v = par[center]; v != -1; v = par[v]) {
            vs.emplace_back(v);
            color[v] = c;
        }
        c++;
    }
    for (const int v : std::views::iota(0, n)) {
        if (color[v] == -1) {
            vs.emplace_back(v);
            color[v] = color[par[v]];
        }
    }
    std::vector<int> index_ptr(c + 1, 0);
    for (const int v : std::views::iota(0, n)) {
        index_ptr[color[v] + 1]++;
    }
    for (const int i : std::views::iota(0, c)) {
        index_ptr[i + 1] += index_ptr[i];
    }
    auto counter = index_ptr;
    std::vector<int> ord(n);
    for (auto v : vs) {
        ord[counter[color[v]]++] = v;
    }
    std::vector<int> relabel(n);
    for (const int v : std::views::iota(0, n)) {
        relabel[ord[v]] = v;
    }
    std::vector<int> original_vs2(n);
    for (const int v : std::views::iota(0, n)) {
        original_vs2[relabel[v]] = original_vs[v];
    }
    std::vector<int> relabel_par(n, -1);
    for (int v : std::views::iota(1, n)) {
        int a = relabel[v];
        int b = relabel[par[v]];
        if (a > b) std::swap(a, b);
        relabel_par[b] = a;
    }
    f(relabel_par, original_vs2, index_ptr);
    for (const int i : std::views::iota(1, c)) {
        int l = index_ptr[i], r = index_ptr[i + 1];
        std::vector<int> par1(r - l, -1);
        std::vector<int> original_vs1(r - l, -1);
        for (int v : std::views::iota(l, r)) {
            par1[v - l] = (relabel_par[v] == 0 ? -1 : relabel_par[v] - l);
            original_vs1[v - l] = original_vs2[v];
        }
        centroid_decomposition_dfs_naive(par1, original_vs1, f);
    }
    return;
}

template <class F>
void one_third_centroid_decomposition(const std::vector<int> &par,
                                      const std::vector<int> &original_vs,
                                      F f) {
    const int n = (int)par.size();
    assert(n > 1);
    if (n == 2) return;
    int center = -1;
    std::vector<int> sz(n, 1);

    for (const int v : std::views::iota(0, n) | std::views::reverse) {
        if (sz[v] >= (n + 1) / 2) {
            center = v;
            break;
        }
        sz[par[v]] += sz[v];
    }

    std::vector<int> color(n, -1);
    std::vector<int> ord(n, -1);
    ord[center] = 0;
    int t = 1;
    int red = n - sz[center];
    for (int v = par[center]; v != -1; v = par[v]) {
        ord[v] = t++;
        color[v] = 0;
    }
    for (const int v : std::views::iota(1, n)) {
        if (par[v] == center && 3 * (red + sz[v]) <= 2 * (n - 1)) {
            red += sz[v];
            ord[v] = t++;
            color[v] = 0;
        }
    }
    for (const int v : std::views::iota(1, n)) {
        if (v != center && color[v] == -1 && color[par[v]] == 0) {
            ord[v] = t++;
            color[v] = 0;
        }
    }
    const int n0 = t - 1;
    for (const int v : std::views::iota(1, n)) {
        if (v != center && color[v] == -1) {
            ord[v] = t++;
            color[v] = 1;
        }
    }
    assert(t == n);
    const int n1 = n - 1 - n0;
    std::vector<int> par0(n0 + 1, -1), par1(n1 + 1, -1), par2(n, -1);
    std::vector<int> original_vs0(n0 + 1), original_vs1(n1 + 1),
        original_vs2(n);
    for (const int i : std::views::iota(0, n)) {
        int v = ord[i];
        original_vs2[v] = original_vs[i];
        if (color[i] != 1) {
            original_vs0[v] = original_vs[i];
        }
        if (color[i] != 0) {
            int idx = std::max(v - n0, 0);
            original_vs1[idx] = original_vs[i];
        }
    }
    for (const int v : std::views::iota(1, n)) {
        int a = ord[v], b = ord[par[v]];
        if (a > b) std::swap(a, b);
        par2[b] = a;
        if (color[v] != 1 && color[par[v]] != 1) {
            par0[b] = a;
        }
        if (color[v] != 0 && color[par[v]] != 0) {
            par1[b - n0] = std::max(a - n0, 0);
        }
    }
    f(par2, original_vs2, n0, n1);
    one_third_centroid_decomposition(par0, original_vs0, f);
    one_third_centroid_decomposition(par1, original_vs1, f);
    return;
}

template <class F>
void one_third_centroid_decomposition_virtual_real(
    const std::vector<int> &par, const std::vector<int> &original_vs,
    const std::vector<int> &is_real, F f) {
    const int n = (int)par.size();
    assert(n > 1);
    if (n == 2) {
        if (is_real[0] && is_real[1]) {
            f(par, original_vs, {0, 1});
        }
        return;
    }
    int center = -1;
    std::vector<int> sz(n, 1);

    for (const int v : std::views::iota(0, n) | std::views::reverse) {
        if (sz[v] >= (n + 1) / 2) {
            center = v;
            break;
        }
        sz[par[v]] += sz[v];
    }

    std::vector<int> color(n, -1);
    std::vector<int> ord(n, -1);
    ord[center] = 0;
    int t = 1;
    int red = n - sz[center];
    for (int v = par[center]; v != -1; v = par[v]) {
        ord[v] = t++;
        color[v] = 0;
    }
    for (const int v : std::views::iota(1, n)) {
        if (par[v] == center && 3 * (red + sz[v]) <= 2 * (n - 1)) {
            red += sz[v];
            ord[v] = t++;
            color[v] = 0;
        }
    }
    for (const int v : std::views::iota(1, n)) {
        if (v != center && color[v] == -1 && color[par[v]] == 0) {
            ord[v] = t++;
            color[v] = 0;
        }
    }
    const int n0 = t - 1;
    for (const int v : std::views::iota(1, n)) {
        if (v != center && color[v] == -1) {
            ord[v] = t++;
            color[v] = 1;
        }
    }
    assert(t == n);
    const int n1 = n - 1 - n0;
    std::vector<int> par0(n0 + 1, -1), par1(n1 + 1, -1), par2(n, -1);
    std::vector<int> original_vs0(n0 + 1), original_vs1(n1 + 1),
        original_vs2(n);
    std::vector<int> is_real0(n0 + 1), is_real1(n1 + 1), is_real2(n);
    for (const int i : std::views::iota(0, n)) {
        int v = ord[i];
        original_vs2[v] = original_vs[i];
        is_real2[v] = is_real[i];
        if (color[i] != 1) {
            original_vs0[v] = original_vs[i];
            is_real0[v] = is_real[i];
        }
        if (color[i] != 0) {
            int idx = std::max(v - n0, 0);
            original_vs1[idx] = original_vs[i];
            is_real1[idx] = is_real[i];
        }
    }
    for (const int v : std::views::iota(1, n)) {
        int a = ord[v], b = ord[par[v]];
        if (a > b) std::swap(a, b);
        par2[b] = a;
        if (color[v] != 1 && color[par[v]] != 1) {
            par0[b] = a;
        }
        if (color[v] != 0 && color[par[v]] != 0) {
            par1[b - n0] = std::max(a - n0, 0);
        }
    }
    if (is_real[center]) {
        color.assign(n, -1);
        color[0] = 0;
        for (const int v : std::views::iota(1, n)) {
            if (is_real2[v]) color[v] = 1;
        }
        f(par2, original_vs2, color);
        is_real0[0] = is_real1[0] = is_real2[0] = 0;
    }
    color.assign(n, -1);
    for (const int v : std::views::iota(1, n)) {
        if (is_real2[v]) {
            color[v] = int(v > n0);
        }
    }
    f(par2, original_vs2, color);
    one_third_centroid_decomposition_virtual_real(par0, original_vs0, is_real0,
                                                  f);
    one_third_centroid_decomposition_virtual_real(par1, original_vs1, is_real1,
                                                  f);
    return;
}

}  // namespace internal

template <int MODE, class F>
void centroid_decomposition(const std::vector<std::vector<int>> &tree, F f) {
    int n = (int)tree.size();
    if (n == 1) return;
    std::vector<int> bfs_order(n), par(n, -1);
    bfs_order[0] = 0;
    int l = 0, r = 1;
    while (l < r) {
        int v = bfs_order[l++];
        for (auto nv : tree[v]) {
            if (nv == par[v]) continue;
            bfs_order[r++] = nv;
            par[nv] = v;
        }
    }
    assert(l == n && r == n);
    {
        std::vector<int> relabel(n);
        for (int i : std::views::iota(0, n)) {
            relabel[bfs_order[i]] = i;
        }
        std::vector<int> relabel_par(n, -1);
        for (int i : std::views::iota(1, n)) {
            relabel_par[relabel[i]] = relabel[par[i]];
        }
        std::swap(par, relabel_par);
    }
    static_assert(MODE == 0 || MODE == 1 || MODE == 2);
    if constexpr (MODE == 0) {
        internal::centroid_decomposition_dfs_naive(par, bfs_order, f);
    } else if constexpr (MODE == 1) {
        internal::one_third_centroid_decomposition(par, bfs_order, f);
    } else {
        internal::one_third_centroid_decomposition_virtual_real(
            par, bfs_order, std::vector<int>(n, 1), f);
    }
}

}  // namespace ebi
#line 2 "math/binomial.hpp"

#line 8 "math/binomial.hpp"

#line 10 "math/binomial.hpp"

namespace ebi {

template <Modint mint> struct Binomial {
  private:
    static void extend(int len = -1) {
        int sz = (int)fact.size();
        if (len < 0)
            len = 2 * sz;
        else
            len = std::max(2 * sz, (int)std::bit_ceil(std::uint32_t(len)));
        len = std::min(len, mint::mod());
        assert(sz <= len);
        fact.resize(len);
        inv_fact.resize(len);
        for (int i : std::views::iota(sz, len)) {
            fact[i] = fact[i - 1] * i;
        }
        inv_fact[len - 1] = fact[len - 1].inv();
        for (int i : std::views::iota(sz, len) | std::views::reverse) {
            inv_fact[i - 1] = inv_fact[i] * i;
        }
    }

  public:
    Binomial() = default;

    Binomial(int n) {
        extend(n + 1);
    }

    static mint f(int n) {
        if (n >= (int)fact.size()) [[unlikely]] {
            extend(n + 1);
        }
        return fact[n];
    }

    static mint inv_f(int n) {
        if (n >= (int)fact.size()) [[unlikely]] {
            extend(n + 1);
        }
        return inv_fact[n];
    }

    static mint c(int n, int r) {
        if (r < 0 || n < r) return 0;
        return f(n) * inv_f(r) * inv_f(n - r);
    }

    static mint p(int n, int r) {
        if (r < 0 || n < r) return 0;
        return f(n) * inv_f(n - r);
    }

    static mint inv(int n) {
        return inv_f(n) * f(n - 1);
    }

    static void reserve(int n) {
        extend(n + 1);
    }

  private:
    static std::vector<mint> fact, inv_fact;
};

template <Modint mint>
std::vector<mint> Binomial<mint>::fact = std::vector<mint>(2, 1);

template <Modint mint>
std::vector<mint> Binomial<mint>::inv_fact = std::vector<mint>(2, 1);

}  // namespace ebi
#line 8 "a.cpp"

namespace ebi {

using mint = modint998244353;

void main_() {
    Binomial<mint> binom(300000);
    int n;
    std::cin >> n;
    std::vector<mint> q(n);
    std::cin >> q;
    graph tree(n);
    auto ans = q;
    rep(i, 0, n - 1) {
        int u, v;
        std::cin >> u >> v;
        u--;
        v--;
        tree.add_edge(u, v);
        ans[u] += q[v] * binom.inv(4);
        ans[v] += q[u] * binom.inv(4);
    }
    auto calc = [&](const std::vector<int> &par, const std::vector<int> &vs,
                    int n0, int n1) {
        int sz = (int)par.size();
        std::vector<int> depth(sz, 0);
        rep(i, 1, sz) {
            depth[i] = depth[par[i]] + 1;
        }
        auto calc2 = [&](int l0, int r0, int l1, int r1) -> void {
            int sz0 = *std::max_element(depth.begin() + l0, depth.begin() + r0);
            int sz1 = *std::max_element(depth.begin() + l1, depth.begin() + r1);
            std::vector<mint> f(sz0 + sz1 +  1), g(sz1 + 1);
            rep(i,0,f.size()) {
                f[i] = binom.inv(i + 1) * binom.inv(i + 1);
            }
            rep(i,l1,r1) {
                g[depth[i]] += q[vs[i]];
            }
            auto h = middle_product<mint, convolution>(f, g);
            assert((int)h.size() == sz0 + 1);
            rep(i,l0,r0) {
                ans[vs[i]] += h[depth[i]];
            }
        };
        calc2(1, 1 + n0, 1 + n0, 1 + n0 + n1);
        calc2(1 + n0, 1 + n0 + n1, 1, 1 + n0);
    };
    centroid_decomposition<1>(tree, calc);
    rep(i,0,n) {
        ans[i] *= binom.f(n) * binom.f(n);
        std::cout << ans[i] << '\n';
    }
}

}  // namespace ebi

int main() {
    ebi::fast_io();
    int t = 1;
    // std::cin >> t;
    while (t--) {
        ebi::main_();
    }
    return 0;
}