//#define NDEBUG
#pragma warning(disable : 4146)

#include <algorithm>
#include <cassert>
#include <cstddef>
#include <cstdint>
#include <iomanip>
#include <ios>
#include <iostream>
#include <utility>
#include <vector>

namespace n91 {

  using i32 = std::int32_t;
  using i64 = std::int64_t;
  using u32 = std::uint32_t;
  using u64 = std::uint64_t;
  using isize = std::ptrdiff_t;
  using usize = std::size_t;
  using f64 = double;

  struct rep {
    struct itr {
      usize i;
      constexpr itr(const usize i) noexcept : i(i) {}
      void operator++() noexcept { ++i; }
      constexpr usize operator*() const noexcept { return i; }
      constexpr bool operator!=(const itr x) const noexcept { return i != x.i; }
    };
    const itr f, l;
    constexpr rep(const usize f, const usize l) noexcept
      : f(std::min(f, l)), l(l) {}
    constexpr auto begin() const noexcept { return f; }
    constexpr auto end() const noexcept { return l; }
  };
  struct revrep {
    struct itr {
      usize i;
      constexpr itr(const usize i) noexcept : i(i) {}
      void operator++() noexcept { --i; }
      constexpr usize operator*() const noexcept { return i; }
      constexpr bool operator!=(const itr x) const noexcept { return i != x.i; }
    };
    const itr f, l;
    constexpr revrep(const usize f, const usize l) noexcept
      : f(l - 1), l(std::min(f, l) - 1) {}
    constexpr auto begin() const noexcept { return f; }
    constexpr auto end() const noexcept { return l; }
  };
  template <class T> auto md_vec(const usize n, const T& value) {
    return std::vector<T>(n, value);
  }
  template <class... Args> auto md_vec(const usize n, Args... args) {
    return std::vector<decltype(md_vec(args...))>(n, md_vec(args...));
  }
  template <class T> constexpr T difference(const T& a, const T& b) noexcept {
    return a < b ? b - a : a - b;
  }
  template <class T> void chmin(T& a, const T& b) noexcept {
    if (b < a)
      a = b;
  }
  template <class T> void chmax(T& a, const T& b) noexcept {
    if (a < b)
      a = b;
  }
  template <class F> class rec_lambda {
    F f;

  public:
    rec_lambda(F&& f_) : f(std::forward<F>(f_)) {}
    template <class... Args> auto operator()(Args &&... args) const {
      return f(*this, std::forward<Args>(args)...);
    }
  };
  template <class T> T scan() {
    T ret;
    std::cin >> ret;
    return ret;
  }
  constexpr char eoln = '\n';

  i64 floor_div(const i64 n, const i64 d) {
    assert(d != 0);
    return n / d - static_cast<i64>((n ^ d) < 0 && n % d != 0);
  }

  i64 ceil_div(const i64 n, const i64 d) {
    assert(d != 0);
    return n / d + static_cast<i64>((n ^ d) >= 0 && n % d != 0);
  }

#ifdef N91_LOCAL
#define OJ_LOCAL(a, b) b
#else
#define OJ_LOCAL(a, b) a
#endif

} // namespace n91

#include <atcoder/convolution>
#include <atcoder/modint>

#include<deque>

namespace n91 {

  void main_() {
    using mint = atcoder::modint998244353;
    const usize n = scan<usize>() + 1;
    const u64 k = scan<u64>();
    std::vector<mint> a(n);
    for (auto& e : a) {
      e = scan<u32>();
    }
    std::vector<std::vector<usize>> g(n);
    for (const usize i : rep(1, n)) {
      g[scan<usize>()].push_back(i);
    }

    std::vector<mint> c(n);
    c[0] = 1;
    for (const usize i : rep(1, std::min<u64>(n, k + 1))) {
      c[i] = c[i - 1] * (k - i + 1) / i;
    }

    const auto back = [&](const std::deque<usize>& p) {
      const usize m = p.size();
      std::vector<mint> b(m);
      for (const usize i : rep(0, m)) {
        b[i] = a[p[m - 1 - i]];
      }
      std::vector<mint> t(c.begin(), c.begin() + m);
      auto conv = atcoder::convolution(b, t);
      conv.resize(m);
      std::reverse(conv.begin(), conv.end());
      return conv;
    };

    std::vector<mint> ans(n, 0);
    auto v =
      rec_lambda([&](const auto& solve, const usize v) -> std::deque<usize> {
      std::deque<usize> t;
      for (const usize ch : g[v]) {
        auto r = solve(ch);
        if (t.size() < r.size()) {
          std::swap(t, r);
        }
        const usize m = r.size();
        const auto conv = back(r);
        for (const usize i : rep(0, m)) {
          ans[r[i]] += conv[i];
          ans[t[i]] -= conv[i];
        }
        for (const usize i : rep(0, m)) {
          a[t[i]] += a[r[i]];
        }
      }
      t.push_front(v);
      return t;
        })(0);
        const auto conv = back(v);
        for (const usize i : rep(0, v.size())) {
          ans[v[i]] += conv[i];
        }

        for (const auto& e : ans) {
          std::cout << e.val() << eoln;
        }
  }

} // namespace n91

int main() {
  //*
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  //*/
  std::cout << std::fixed << std::setprecision(20);
  n91::main_();
  return 0;
}