結果

問題 No.1145 Sums of Powers
ユーザー risujiroh
提出日時 2020-07-08 17:44:35
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 320 ms / 2,000 ms
コード長 4,232 bytes
コンパイル時間 2,392 ms
コンパイル使用メモリ 209,300 KB
最終ジャッジ日時 2025-01-11 17:00:01
ジャッジサーバーID
（参考情報） 		judge5 / judge2
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ファイルパターン 結果
other AC * 6
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ソースコード

diff #
プレゼンテーションモードにする

#include <bits/stdc++.h>
using namespace std;
template <class T, class Op = multiplies<T>>
constexpr T power(T a, long long n, Op op = Op(), T e = {1}) {
  assert(n >= 0);
  while (n) {
    if (n & 1) e = op(e, a);
    if (n >>= 1) a = op(a, a);
  }
  return e;
}
template <class T> void ntt(vector<T>& a, bool inverse) {
  int n = size(a);
  assert((n & (n - 1)) == 0);
  if (n < 2) return;
  assert((T::mod - 1) % n == 0);
  static vector<T> w{1}, iw{1};
  for (int m = size(w); m < n / 2; m *= 2) {
    static T root = 2;
    while (power(root, (T::mod - 1) / 2) == 1) root += 1;
    T dw = power(root, (T::mod - 1) / (4 * m)), idw = 1 / dw;
    w.resize(2 * m), iw.resize(2 * m);
    for (int i = 0; i < m; ++i) w[m + i] = w[i] * dw, iw[m + i] = iw[i] * idw;
  }
  if (not inverse) {
    for (int m = n; m >>= 1; ) {
      for (int s = 0, k = 0; s < n; s += 2 * m, ++k) {
        for (int i = s, j = s + m; i < s + m; ++i, ++j) {
          T x = a[i], y = a[j] * w[k];
          a[i] = x + y, a[j] = x - y;
        }
      }
    }
  } else {
    for (int m = 1; m < n; m *= 2) {
      for (int s = 0, k = 0; s < n; s += 2 * m, ++k) {
        for (int i = s, j = s + m; i < s + m; ++i, ++j) {
          T x = a[i], y = a[j];
          a[i] = x + y, a[j] = (x - y) * iw[k];
        }
      }
    }
    auto inv = 1 / T(n);
    for (auto&& e : a) e *= inv;
  }
}
template <class T> vector<T> operator*(vector<T> a, vector<T> b) {
  if (empty(a) or empty(b)) return {};
  int n = size(a), m = size(b), sz = 1 << __lg(2 * (n + m - 1) - 1);
  a.resize(sz), ntt(a, false);
  b.resize(sz), ntt(b, false);
  for (int i = 0; i < sz; ++i) a[i] *= b[i];
  ntt(a, true), a.resize(n + m - 1);
  return a;
}
template <class T> vector<T> operator-(vector<T> a) {
  for (auto&& e : a) e = -e;
  return a;
}
template <class T> vector<T>& operator*=(vector<T>& a, const vector<T>& b) {
  return a = a * b;
}
template <class T> vector<T> inverse(const vector<T>& a) {
  assert(not empty(a) and not (a[0] == 0));
  vector<T> b{1 / a[0]};
  while (size(b) < size(a)) {
    vector<T> x(begin(a), begin(a) + min(size(a), 2 * size(b)));
    x *= b * b;
    b.resize(2 * size(b));
    for (auto i = size(b) / 2; i < min(size(x), size(b)); ++i) b[i] = -x[i];
  }
  return {begin(b), begin(b) + size(a)};
}
template <class T> vector<T> derivative(const vector<T>& a) {
  vector<T> res(max((int)size(a) - 1, 0));
  for (int i = 0; i < (int)size(res); ++i) res[i] = (i + 1) * a[i + 1];
  return res;
}
template <class T> vector<T> primitive(const vector<T>& a) {
  vector<T> res(size(a) + 1);
  for (int i = 1; i < (int)size(res); ++i) res[i] = a[i - 1] / i;
  return res;
}
template <class T> vector<T> logarithm(const vector<T>& a) {
  assert(not empty(a) and a[0] == 1);
  auto res = primitive(derivative(a) * inverse(a));
  return {begin(res), begin(res) + size(a)};
}
template <unsigned M> struct modular {
  using m = modular;
  static constexpr unsigned mod = M;
  unsigned v;
  modular(long long x = 0) : v((x %= mod) < 0 ? x + mod : x) {}
  m operator-() const { return m() -= *this; }
  m& operator+=(m b) { if ((int)(v += b.v - mod) < 0) v += mod; return *this; }
  m& operator-=(m b) { if ((int)(v -= b.v) < 0) v += mod; return *this; }
  m& operator*=(m b) { v = (uint64_t)v * b.v % mod; return *this; }
  m& operator/=(m b) { return *this *= power(b, mod - 2); }
  friend m operator+(m a, m b) { return a += b; }
  friend m operator-(m a, m b) { return a -= b; }
  friend m operator*(m a, m b) { return a *= b; }
  friend m operator/(m a, m b) { return a /= b; }
  friend bool operator==(m a, m b) { return a.v == b.v; }
};
using mint = modular<998244353>;
int main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  int n, m;
  cin >> n >> m;
  vector<vector<mint>> tree(2 * n);
  for (int i = 0; i < n; ++i) {
    int a;
    cin >> a;
    tree[n + i] = {1, -a};
  }
  for (int i = n; i-- > 1; ) {
    tree[i] = tree[2 * i] * tree[2 * i + 1];
  }
  auto f = tree[1];
  f.resize(m + 1);
  f = -logarithm(f);
  for (int k = 1; k <= m; ++k) {
    f[k] *= k;
    cout << f[k].v << " \n"[k == m];
  }
}
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