結果

問題 No.931 Multiplicative Convolution
コンテスト
ユーザー emthrm
提出日時 2021-03-02 02:56:54
言語 C++17
(gcc 13.3.0 + boost 1.89.0)
結果
AC  
実行時間 147 ms / 2,000 ms
コード長 10,047 bytes
記録
記録タグの例:
初AC ショートコード 純ショートコード 純主流ショートコード 最速実行時間
コンパイル時間 2,229 ms
コンパイル使用メモリ 213,740 KB
最終ジャッジ日時 2025-01-19 09:08:50
ジャッジサーバーID
（参考情報） 		judge1 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 14
権限があれば一括ダウンロードができます

ソースコード

diff #
raw source code 

#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
using ll = long long;
constexpr int INF = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
constexpr double EPS = 1e-8;
constexpr int MOD = 1000000007;
// constexpr int MOD = 998244353;
constexpr int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1};
constexpr int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1}, dx8[] = {0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U> inline bool chmax(T &a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U> inline bool chmin(T &a, U b) { return a > b ? (a = b, true) : false; }
struct IOSetup {
  IOSetup() {
    std::cin.tie(nullptr);
    std::ios_base::sync_with_stdio(false);
    std::cout << fixed << setprecision(20);
  }
} iosetup;

template <int ID>
struct MInt {
  unsigned int val;
  MInt(): val(0) {}
  MInt(long long x) : val(x >= 0 ? x % mod() : x % mod() + mod()) {}
  static int get_mod() { return mod(); }
  static void set_mod(int divisor) { mod() = divisor; }
  static void init(int x = 10000000) { inv(x, true); fact(x); fact_inv(x); }
  static MInt inv(int x, bool init = false) {
    // assert(0 <= x && x < mod() && std::__gcd(x, mod()) == 1);
    static std::vector<MInt> inverse{0, 1};
    int prev = inverse.size();
    if (init && x >= prev) {
      // "x!" and "mod()" must be disjoint.
      inverse.resize(x + 1);
      for (int i = prev; i <= x; ++i) inverse[i] = -inverse[mod() % i] * (mod() / i);
    }
    if (x < inverse.size()) return inverse[x];
    unsigned int a = x, b = mod(); int u = 1, v = 0;
    while (b) {
      unsigned int tmp = a / b;
      std::swap(a -= tmp * b, b);
      std::swap(u -= tmp * v, v);
    }
    return u;
  }
  static MInt fact(int x) {
    static std::vector<MInt> f{1};
    int prev = f.size();
    if (x >= prev) {
      f.resize(x + 1);
      for (int i = prev; i <= x; ++i) f[i] = f[i - 1] * i;
    }
    return f[x];
  }
  static MInt fact_inv(int x) {
    static std::vector<MInt> finv{1};
    int prev = finv.size();
    if (x >= prev) {
      finv.resize(x + 1);
      finv[x] = inv(fact(x).val);
      for (int i = x; i > prev; --i) finv[i - 1] = finv[i] * i;
    }
    return finv[x];
  }
  static MInt nCk(int n, int k) {
    if (n < 0 || n < k || k < 0) return 0;
    if (n - k > k) k = n - k;
    return fact(n) * fact_inv(k) * fact_inv(n - k);
  }
  static MInt nPk(int n, int k) { return n < 0 || n < k || k < 0 ? 0 : fact(n) * fact_inv(n - k); }
  static MInt nHk(int n, int k) { return n < 0 || k < 0 ? 0 : (k == 0 ? 1 : nCk(n + k - 1, k)); }
  MInt pow(long long exponent) const {
    MInt tmp = *this, res = 1;
    while (exponent > 0) {
      if (exponent & 1) res *= tmp;
      tmp *= tmp;
      exponent >>= 1;
    }
    return res;
  }
  MInt &operator+=(const MInt &x) { if((val += x.val) >= mod()) val -= mod(); return *this; }
  MInt &operator-=(const MInt &x) { if((val += mod() - x.val) >= mod()) val -= mod(); return *this; }
  MInt &operator*=(const MInt &x) { val = static_cast<unsigned long long>(val) * x.val % mod(); return *this; }
  MInt &operator/=(const MInt &x) { return *this *= inv(x.val); }
  bool operator==(const MInt &x) const { return val == x.val; }
  bool operator!=(const MInt &x) const { return val != x.val; }
  bool operator<(const MInt &x) const { return val < x.val; }
  bool operator<=(const MInt &x) const { return val <= x.val; }
  bool operator>(const MInt &x) const { return val > x.val; }
  bool operator>=(const MInt &x) const { return val >= x.val; }
  MInt &operator++() { if (++val == mod()) val = 0; return *this; }
  MInt operator++(int) { MInt res = *this; ++*this; return res; }
  MInt &operator--() { val = (val == 0 ? mod() : val) - 1; return *this; }
  MInt operator--(int) { MInt res = *this; --*this; return res; }
  MInt operator+() const { return *this; }
  MInt operator-() const { return MInt(val ? mod() - val : 0); }
  MInt operator+(const MInt &x) const { return MInt(*this) += x; }
  MInt operator-(const MInt &x) const { return MInt(*this) -= x; }
  MInt operator*(const MInt &x) const { return MInt(*this) *= x; }
  MInt operator/(const MInt &x) const { return MInt(*this) /= x; }
  friend std::ostream &operator<<(std::ostream &os, const MInt &x) { return os << x.val; }
  friend std::istream &operator>>(std::istream &is, MInt &x) { long long val; is >> val; x = MInt(val); return is; }
private:
  static int &mod() { static int divisor = 0; return divisor; }
};
namespace std { template <int ID> MInt<ID> abs(const MInt<ID> &x) { return x; } }

long long euler_phi(long long n) {
  assert(n >= 1);
  long long res = n;
  for (long long i = 2; i * i <= n; ++i) {
    if (n % i == 0) {
      res -= res / i;
      while (n % i == 0) n /= i;
    }
  }
  if (n > 1) res -= res / n;
  return res;
}

template <typename T>
std::vector<std::pair<T, int>> prime_factorization(T n) {
  std::vector<std::pair<T, int>> res;
  for (T i = 2; i * i <= n; ++i) {
    if (n % i != 0) continue;
    int exponent = 0;
    while (n % i == 0) {
      ++exponent;
      n /= i;
    }
    res.emplace_back(i, exponent);
  }
  if (n != 1) res.emplace_back(n, 1);
  return res;
}

long long mod_pow(long long base, long long exponent, int mod) {
  base %= mod;
  long long res = 1;
  while (exponent > 0) {
    if (exponent & 1) (res *= base) %= mod;
    (base *= base) %= mod;
    exponent >>= 1;
  }
  return res;
}

bool is_primitive_root(long long root, long long m) {
  if ((root %= m) < 0) root += m;
  if (std::__gcd(root, m) > 1) return false;
  long long phi = euler_phi(m);
  for (const std::pair<long long, long long> &pr : prime_factorization(phi)) {
    if (mod_pow(root, phi / pr.first, m) == 1) return false;
  }
  return true;
}

template <int T>
struct NTT {
  using ModInt = MInt<T>;

  NTT() {
    for (int i = 0; i < 23; ++i) {
      if (primes[i][0] == ModInt::get_mod()) {
        n_max = 1 << primes[i][2];
        root = ModInt(primes[i][1]).pow((ModInt::get_mod() - 1) >> primes[i][2]);
        return;
      }
    }
    assert(false);
  }

  void sub_dft(std::vector<ModInt> &a) {
    int n = a.size();
    assert(__builtin_popcount(n) == 1);
    calc(n);
    int shift = __builtin_ctz(butterfly.size()) - __builtin_ctz(n);
    for (int i = 0; i < n; ++i) {
      int j = butterfly[i] >> shift;
      if (i < j) std::swap(a[i], a[j]);
    }
    for (int block = 1; block < n; block <<= 1) {
      int den = __builtin_ctz(block);
      for (int i = 0; i < n; i += (block << 1)) for (int j = 0; j < block; ++j) {
        ModInt tmp = a[i + j + block] * omega[den][j];
        a[i + j + block] = a[i + j] - tmp;
        a[i + j] += tmp;
      }
    }
  }

  template <typename U>
  std::vector<ModInt> dft(const std::vector<U> &a) {
    int n = a.size(), lg = 1;
    while ((1 << lg) < n) ++lg;
    std::vector<ModInt> A(1 << lg, 0);
    for (int i = 0; i < n; ++i) A[i] = a[i];
    sub_dft(A);
    return A;
  }

  void idft(std::vector<ModInt> &a) {
    int n = a.size();
    assert(__builtin_popcount(n) == 1);
    sub_dft(a);
    std::reverse(a.begin() + 1, a.end());
    ModInt inv_n = ModInt::inv(n);
    for (int i = 0; i < n; ++i) a[i] *= inv_n;
  }

  template <typename U>
  std::vector<ModInt> convolution(const std::vector<U> &a, const std::vector<U> &b) {
    int a_sz = a.size(), b_sz = b.size(), sz = a_sz + b_sz - 1, lg = 1;
    while ((1 << lg) < sz) ++lg;
    int n = 1 << lg;
    std::vector<ModInt> A(n, 0), B(n, 0);
    for (int i = 0; i < a_sz; ++i) A[i] = a[i];
    for (int i = 0; i < b_sz; ++i) B[i] = b[i];
    sub_dft(A);
    sub_dft(B);
    for (int i = 0; i < n; ++i) A[i] *= B[i];
    idft(A);
    A.resize(sz);
    return A;
  }

private:
  int primes[23][3]{
    {16957441, 329, 14},
    {17006593, 26, 15},
    {19529729, 770, 17},
    {167772161, 3, 25},
    {469762049, 3, 26},
    {645922817, 3, 23},
    {897581057, 3, 23},
    {924844033, 5, 21},
    {935329793, 3, 22},
    {943718401, 7, 22},
    {950009857, 7, 21},
    {962592769, 7, 21},
    {975175681, 17, 21},
    {976224257, 3, 20},
    {985661441, 3, 22},
    {998244353, 3, 23},
    {1004535809, 3, 21},
    {1007681537, 3, 20},
    {1012924417, 5, 21},
    {1045430273, 3, 20},
    {1051721729, 6, 20},
    {1053818881, 7, 20},
    {1224736769, 3, 24}
  };

  int n_max;
  ModInt root;
  std::vector<int> butterfly{0};
  std::vector<std::vector<ModInt>> omega{{1}};

  void calc(int n) {
    int prev_n = butterfly.size();
    if (n <= prev_n) return;
    assert(n <= n_max);
    butterfly.resize(n);
    int prev_lg = omega.size(), lg = __builtin_ctz(n);
    for (int i = 1; i < prev_n; ++i) butterfly[i] <<= lg - prev_lg;
    for (int i = prev_n; i < n; ++i) butterfly[i] = (butterfly[i >> 1] >> 1) | ((i & 1) << (lg - 1));
    omega.resize(lg);
    for (int i = prev_lg; i < lg; ++i) {
      omega[i].resize(1 << i);
      ModInt tmp = root.pow((ModInt::get_mod() - 1) / (1 << (i + 1)));
      for (int j = 0; j < (1 << (i - 1)); ++j) {
        omega[i][j << 1] = omega[i - 1][j];
        omega[i][(j << 1) + 1] = omega[i - 1][j] * tmp;
      }
    }
  }
};

int main() {
  int p;
  std::cin >> p;
  MInt<0>::set_mod(p);
  std::vector<MInt<0>> memo(p - 1);
  for (int root = 2; ; ++root) {
    if (is_primitive_root(root, p)) {
      for (int i = 0; i < p - 1; ++i) memo[i] = MInt<0>(root).pow(i);
      break;
    }
  }
  std::vector<int> a(p, 0), b(p, 0);
  for (int i = 1; i < p; ++i) std::cin >> a[i];
  for (int i = 1; i < p; ++i) std::cin >> b[i];
  MInt<1>::set_mod(998244353);
  NTT<1> ntt;
  std::vector<MInt<1>> A(p - 1, 0), B(p - 1, 0);
  for (int i = 0; i < p - 1; ++i) {
    A[i] = a[memo[i].val];
    B[i] = b[memo[i].val];
  }
  std::vector<MInt<1>> C = ntt.convolution(A, B);
  for (int i = p - 1; i < C.size(); ++i) C[i % (p - 1)] += C[i];
  std::vector<MInt<1>> ans(p, 0);
  for (int i = 0; i < p - 1; ++i) ans[memo[i].val] = C[i];
  for (int i = 1; i < p; ++i) std::cout << ans[i] << " \n"[i + 1 == p];
  return 0;
}
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