#687416 (C++14) No.1145 Sums of Powers

• 問題: No.1145 Sums of Powers
• ユーザー: Aoxiang Cui
• 提出日時: 2021-08-08 09:56:42
• 言語: C++14 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 514 ms / 2,000 ms
• コード長: 8,396 bytes
• コンパイル時間: 1,673 ms
• コンパイル使用メモリ: 128,520 KB
• 実行使用メモリ: 10,708 KB
• 最終ジャッジ日時: 2024-09-19 05:43:20
• 合計ジャッジ時間: 3,897 ms
• ジャッジサーバーID （参考情報）: judge1 / judge3

ファイルパターン	結果
other	AC * 6

ソースコード

// #define LOCAL
#define _USE_MATH_DEFINES
#include <array>
#include <cassert>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <iomanip>
#include <string>
#include <sstream>
#include <vector>
#include <queue>
#include <stack>
#include <list>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <algorithm>
#include <complex>
#include <cmath>
#include <numeric>
#include <bitset>
#include <functional>
#include <random>
#include <ctime>

using namespace std;

template <typename A, typename B>
ostream& operator <<(ostream& out, const pair<A, B>& a) {
  out << "(" << a.first << "," << a.second << ")";
  return out;
}
template <typename T, size_t N>
ostream& operator <<(ostream& out, const array<T, N>& a) {
  out << "["; bool first = true;
  for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "]";
  return out;
}
template <typename T>
ostream& operator <<(ostream& out, const vector<T>& a) {
  out << "["; bool first = true;
  for (auto v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "]";
  return out;
}
template <typename T, class Cmp>
ostream& operator <<(ostream& out, const set<T, Cmp>& a) {
  out << "{"; bool first = true;
  for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "}";
  return out;
}
template <typename U, typename T, class Cmp>
ostream& operator <<(ostream& out, const map<U, T, Cmp>& a) {
  out << "{"; bool first = true;
  for (auto& p : a) { out << (first ? "" : ", "); out << p.first << ":" << p.second; first = 0;} out << "}";
  return out;
}
#ifdef LOCAL
#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
#else
#define trace(...) 42
#endif
template <typename Arg1>
void __f(const char* name, Arg1&& arg1){
  cerr << name << ": " << arg1 << endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args){
  const char* comma = strchr(names + 1, ',');
  cerr.write(names, comma - names) << ": " << arg1 << " |";
  __f(comma + 1, args...);
}

template <class T> auto vect(const T& v, int n) { return vector<T>(n, v); }
template <class T, class... D> auto vect(const T& v, int n, D... m) {
  return vector<decltype(vect(v, m...))>(n, vect(v, m...));
}

typedef long long int64;
typedef pair<int, int> ii;
#define SZ(x) (int)((x).size())
template <typename T> static constexpr T inf = numeric_limits<T>::max() / 2;
// const int MOD = 1e9 + 7;
const int MOD = 998244353;
mt19937 mrand(random_device{}());
int rnd(int x) { return mrand() % x; }
// mt19937_64 mrand(random_device{}());
// int64 rnd(int64 x) { return mrand() % x; }
template <class T> void out(const vector<T>& a) { for (int i = 0; i < SZ(a); ++i) cout << a[i] << " \n"[i + 1 == SZ(a)]; }
template <class T> bool ckmin(T& a, const T& b) { return b < a ? a = b, 1 : 0; }
template <class T> bool ckmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; }
template <class T> void dedup(vector<T>& v) { sort(v.begin(), v.end()); v.erase(unique(v.begin(), v.end()), v.end()); }
void add(int& x, int y) { x += y; if (x >= MOD) x -= MOD; }

struct fast_ios {
  fast_ios() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
  };
} fast_ios_;

// const int MOD = 998244353; // prime, 2^23*7*17+1
typedef int atom;
const int G = 3;

int64 power_mod(int64 a, int64 n, int p = MOD) {
  int64 ret = 1;
  for (; n; n >>= 1) {
    if (n & 1) ret = ret * a % p;
    a = a * a % p;
  }
  return ret;
}

int64 inv_mod(int64 a) {
  return power_mod(a, MOD - 2);
}

void bit_reverse(vector<atom>& a) {
  int n = a.size();
  for (int i = 1, j = n / 2; i < n - 1; ++i) {
    if (i < j) swap(a[i], a[j]);
    int k = n / 2;
    while (j >= k) j -= k, k /= 2;
    if (j < k) j += k;
  }
}

void fft(vector<atom>& a, int flag) {
  int n = a.size();
  bit_reverse(a);
  vector<atom> wn(n);
  wn[0] = 1;
  wn[1] = power_mod(G, flag == 1 ? (MOD - 1) / n : MOD - 1 - (MOD - 1) / n);
  for (int i = 2; i < n; ++i) wn[i] = (int64)wn[i - 1] * wn[1] % MOD;
  for (int k = 2; k <= n; k <<= 1) {
    for (int i = 0; i < n; i += k) {
      int wi = 0, step = n / k;
      for (int j = i; j < i + k / 2; ++j) {
        atom u = a[j];
        atom v = (int64)wn[wi] * a[j + k / 2] % MOD;
        a[j] = (u + v) % MOD;
        a[j + k / 2] = (u + MOD - v) % MOD;
        wi += step;
      }
    }
  }
  if (flag < 0) {
    int64 inv_n = inv_mod(n);
    for (int i = 0; i < n; ++i) a[i] = a[i] * inv_n % MOD;
  }
}

namespace polynomial {

vector<int> mul(const vector<int>& f, const vector<int>& g, int cap = inf<int>) {
  int n = f.size(), m = g.size();
  int len = 1;
  while (len < n + m - 1) len <<= 1;
  vector<atom> x(len), y(len);
  copy(f.begin(), f.end(), x.begin());
  copy(g.begin(), g.end(), y.begin());
  fft(x, 1);
  fft(y, 1);
  for (int i = 0; i < len; ++i) x[i] = (int64)x[i] * y[i] % MOD;
  fft(x, -1);
  cap = min(cap, n + m - 1);
  x.resize(cap);
  return x;
}

vector<int> differential(const vector<int>& f) {
  int n = f.size();
  vector<int> ret(n);
  for (int i = 0; i < n - 1; ++i) ret[i] = (int64)f[i + 1] * (i + 1) % MOD;
  return ret;
}

void integral(vector<int>& f) {
  int n = f.size();
  for (int i = n - 1; i > 0; --i) f[i] = inv_mod(i) * f[i - 1] % MOD;
  f[0] = 0;
}

// g:=g*(2-f*g), n is power of 2
vector<int> inverse(const vector<int>& f) {
  int n = f.size();
  if (n == 1) return {(int)inv_mod(f[0])};
  vector<int> f1(f.begin(), f.begin() + (n >> 1));
  auto g = inverse(f1);
  g.resize(n);
  auto h = mul(f, g, n);
  h[0] = (2 + MOD - h[0]) % MOD;
  for (int i = 1; i < h.size(); ++i) h[i] = (MOD - h[i]) % MOD;
  return mul(h, g, n);
}

pair<vector<int>, vector<int>> div(const vector<int>& f, const vector<int>& g) {
  int n = f.size(), m = g.size();
  int k = n - m + 1;
  if (n < m) return make_pair(vector<int>{0}, f);
  int len = 1;
  while (len < m) len <<= 1;
  vector<int> fr(n), gr(len);
  copy(f.rbegin(), f.rend(), fr.begin());
  copy(g.rbegin(), g.rend(), gr.begin());
  auto h = inverse(gr);
  h = mul(fr, h);
  vector<int> d(k);
  for (int i = 0; i < k; ++i) d[i] = h[k - 1 - i];
  h = mul(g, d);
  vector<int> r(m);
  for (int i = 0; i < m; ++i) r[i] = (f[i] + MOD - h[i]) % MOD;
  int deg_r = m - 1;
  while (deg_r && r[deg_r] == 0) --deg_r;
  r.resize(deg_r + 1);
  return make_pair(d, r);
}

int64 W;
ii operator *(const ii& u, const ii& v) {
  return {((int64)u.first * v.first + (int64)u.second * v.second % MOD * W) % MOD,
    ((int64)u.first * v.second + (int64)u.second * v.first) % MOD};
}

ii power_mod(ii a, int64 n) {
  ii ret = {1, 0};
  for (; n; n >>= 1) {
    if (n & 1) ret = ret * a;
    a = a * a;
  }
  return ret;
}

int cipolla(int x) {
  int y;
  while (true) {
    y = rnd(MOD);
    W = ((int64)y * y % MOD + MOD - x) % MOD;
    if (::power_mod(W, (MOD - 1) / 2) > 1) break;
  }
  ii ret(y, 1);
  ret = power_mod(ret, (MOD + 1) / 2);
  return min(ret.first, MOD - ret.first);
}

// g:=(g+f/g)/2, n is power of 2
vector<int> sqrt(const vector<int>& f) {
  int n = f.size();
  if (n == 1) return {cipolla(f[0])};
  vector<int> f1(f.begin(), f.begin() + (n >> 1));
  auto g = sqrt(f1);
  g.resize(n);
  auto h = inverse(g);
  h = mul(f, h, n);
  int64 inv2 = inv_mod(2);
  for (int i = 0; i < n; ++i) g[i] = (g[i] + h[i]) * inv2 % MOD;
  return g;
}

// g=integral(f'/f), n is power of 2
vector<int> log(const vector<int>& f) {
  auto g = differential(f);
  auto h = inverse(f);
  auto ret = mul(g, h);
  ret.resize(f.size());
  integral(ret);
  return ret;
}

// g:=g*(1-log(g)+f), n is power of 2
vector<int> exp(const vector<int>& f) {
  int n = f.size();
  if (n == 1) return vector<int>{1};
  vector<int> f1(f.begin(), f.begin() + (n >> 1));
  auto g = exp(f1);
  g.resize(n);
  auto h = log(g);
  for (int i = 0; i < n; ++i) h[i] = ((i == 0) + f[i] + MOD - h[i]) % MOD;
  return mul(g, h, n);
}
}

using namespace polynomial;

const int N = 1e5 + 10;
int a[N];

vector<int> solve(int L, int R) {
  if (L + 1 == R) return {1, MOD - a[L]};
  int mid = (L + R) / 2;
  return mul(solve(L, mid), solve(mid, R));
}

int main() {
  int n, m;
  cin >> n >> m;
  for (int i = 0; i < n; ++i) cin >> a[i];

  auto f = solve(0, n);
  trace(f);

  int len = 1;
  while (len <= m) len *= 2;
  f.resize(len);
  f = log(f);

  vector<int> ret(m);
  for (int k = 1; k <= m; ++k) {
    ret[k - 1] = (MOD - 1LL * f[k] * k % MOD) % MOD;
  }
  out(ret);
  return 0;
}