結果

問題 No.931 Multiplicative Convolution
ユーザー HaarHaar
提出日時 2020-11-07 04:47:26
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 63 ms / 2,000 ms
コード長 9,723 bytes
コンパイル時間 3,578 ms
コンパイル使用メモリ 216,452 KB
実行使用メモリ 8,832 KB
最終ジャッジ日時 2024-07-22 14:18:12
合計ジャッジ時間 4,337 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
5,248 KB
testcase_01 AC 2 ms
5,376 KB
testcase_02 AC 2 ms
5,376 KB
testcase_03 AC 2 ms
5,376 KB
testcase_04 AC 2 ms
5,376 KB
testcase_05 AC 2 ms
5,376 KB
testcase_06 AC 2 ms
5,376 KB
testcase_07 AC 8 ms
5,376 KB
testcase_08 AC 63 ms
8,832 KB
testcase_09 AC 48 ms
8,704 KB
testcase_10 AC 60 ms
8,448 KB
testcase_11 AC 50 ms
8,448 KB
testcase_12 AC 51 ms
7,552 KB
testcase_13 AC 61 ms
8,576 KB
testcase_14 AC 63 ms
8,704 KB
testcase_15 AC 62 ms
8,704 KB
testcase_16 AC 62 ms
8,576 KB
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ソースコード

diff # 

#line 1 "main.cpp"
#include <bits/stdc++.h>

#line 4 "/home/haar/Downloads/kyopro-lib/Mylib/Number/Mint/mint.cpp"

namespace haar_lib {
  template <int32_t M>
  class modint {
    uint32_t val_;

  public:
    constexpr static auto mod(){return M;}

    constexpr modint(): val_(0){}
    constexpr modint(int64_t n){
      if(n >= M) val_ = n % M;
      else if(n < 0) val_ = n % M + M;
      else val_ = n;
    }

    constexpr auto& operator=(const modint &a){val_ = a.val_; return *this;}
    constexpr auto& operator+=(const modint &a){
      if(val_ + a.val_ >= M) val_ = (uint64_t)val_ + a.val_ - M;
      else val_ += a.val_;
      return *this;
    }
    constexpr auto& operator-=(const modint &a){
      if(val_ < a.val_) val_ += M;
      val_ -= a.val_;
      return *this;
    }
    constexpr auto& operator*=(const modint &a){
      val_ = (uint64_t)val_ * a.val_ % M;
      return *this;
    }
    constexpr auto& operator/=(const modint &a){
      val_ = (uint64_t)val_ * a.inv().val_ % M;
      return *this;
    }

    constexpr auto operator+(const modint &a) const {return modint(*this) += a;}
    constexpr auto operator-(const modint &a) const {return modint(*this) -= a;}
    constexpr auto operator*(const modint &a) const {return modint(*this) *= a;}
    constexpr auto operator/(const modint &a) const {return modint(*this) /= a;}

    constexpr bool operator==(const modint &a) const {return val_ == a.val_;}
    constexpr bool operator!=(const modint &a) const {return val_ != a.val_;}

    constexpr auto& operator++(){*this += 1; return *this;}
    constexpr auto& operator--(){*this -= 1; return *this;}

    constexpr auto operator++(int){auto t = *this; *this += 1; return t;}
    constexpr auto operator--(int){auto t = *this; *this -= 1; return t;}

    constexpr static modint pow(int64_t n, int64_t p){
      if(p < 0) return pow(n, -p).inv();

      int64_t ret = 1, e = n % M;
      for(; p; (e *= e) %= M, p >>= 1) if(p & 1) (ret *= e) %= M;
      return ret;
    }

    constexpr static modint inv(int64_t a){
      int64_t b = M, u = 1, v = 0;

      while(b){
        int64_t t = a / b;
        a -= t * b; std::swap(a, b);
        u -= t * v; std::swap(u, v);
      }

      u %= M;
      if(u < 0) u += M;

      return u;
    }

    constexpr static auto frac(int64_t a, int64_t b){return modint(a) / modint(b);}

    constexpr auto pow(int64_t p) const {return pow(val_, p);}
    constexpr auto inv() const {return inv(val_);}

    friend constexpr auto operator-(const modint &a){return modint(M - a.val_);}

    friend constexpr auto operator+(int64_t a, const modint &b){return modint(a) + b;}
    friend constexpr auto operator-(int64_t a, const modint &b){return modint(a) - b;}
    friend constexpr auto operator*(int64_t a, const modint &b){return modint(a) * b;}
    friend constexpr auto operator/(int64_t a, const modint &b){return modint(a) / b;}

    friend std::istream& operator>>(std::istream &s, modint &a){s >> a.val_; return s;}
    friend std::ostream& operator<<(std::ostream &s, const modint &a){s << a.val_; return s;}

    template <int N>
    static auto div(){
      static auto value = inv(N);
      return value;
    }

    explicit operator int32_t() const noexcept {return val_;}
    explicit operator int64_t() const noexcept {return val_;}
  };
}
#line 7 "/home/haar/Downloads/kyopro-lib/Mylib/Convolution/ntt_convolution.cpp"

namespace haar_lib {
  template <typename T, int PRIM_ROOT, int MAX_SIZE>
  class number_theoretic_transform {
  public:
    using value_type = T;
    constexpr static int primitive_root = PRIM_ROOT;
    constexpr static int max_size = MAX_SIZE;

  private:
    const int MAX_POWER_;
    std::vector<T> BASE_, INV_BASE_;

  public:
    number_theoretic_transform():
      MAX_POWER_(__builtin_ctz(MAX_SIZE)),
      BASE_(MAX_POWER_ + 1),
      INV_BASE_(MAX_POWER_ + 1)
    {
      static_assert((MAX_SIZE & (MAX_SIZE - 1)) == 0, "MAX_SIZE must be power of 2.");

      T t = T::pow(PRIM_ROOT, (T::mod() - 1) >> (MAX_POWER_ + 2));
      T s = t.inv();

      for(int i = MAX_POWER_; --i >= 0;){
        t *= t;
        s *= s;
        BASE_[i] = -t;
        INV_BASE_[i] = -s;
      }
    }

    void run(std::vector<T> &f, bool INVERSE = false) const {
      const int n = f.size();
      assert((n & (n - 1)) == 0 and n <= MAX_SIZE); // データ数は2の冪乗個

      if(INVERSE){
        for(int b = 1; b < n; b <<= 1){
          T w = 1;
          for(int j = 0, k = 1; j < n; j += 2 * b, ++k){
            for(int i = 0; i < b; ++i){
              const auto s = f[i + j];
              const auto t = f[i + j + b];

              f[i + j] = s + t;
              f[i + j + b] = (s - t) * w;
            }
            w *= INV_BASE_[__builtin_ctz(k)];
          }
        }

        const T t = T::inv(n);
        for(auto &x : f) x *= t;
      }else{
        for(int b = n >> 1; b; b >>= 1){
          T w = 1;
          for(int j = 0, k = 1; j < n; j += 2 * b, ++k){
            for(int i = 0; i < b; ++i){
              const auto s = f[i + j];
              const auto t = f[i + j + b] * w;

              f[i + j] = s + t;
              f[i + j + b] = s - t;
            }
            w *= BASE_[__builtin_ctz(k)];
          }
        }
      }
    }

    template <typename U>
    std::vector<T> convolve(std::vector<U> f, std::vector<U> g) const {
      const int m = f.size() + g.size() - 1;
      int n = 1;
      while(n < m) n *= 2;

      std::vector<T> f2(n), g2(n);

      for(int i = 0; i < (int)f.size(); ++i) f2[i] = (int64_t)f[i];
      for(int i = 0; i < (int)g.size(); ++i) g2[i] = (int64_t)g[i];

      run(f2);
      run(g2);

      for(int i = 0; i < n; ++i) f2[i] *= g2[i];
      run(f2, true);

      return f2;
    }

    template <typename U>
    std::vector<T> operator()(std::vector<U> f, std::vector<U> g) const {
      return convolve(f, g);
    }
  };

  template <typename T>
  std::vector<T> convolve_general_mod(std::vector<T> f, std::vector<T> g){
    static constexpr int M1 = 167772161, P1 = 3;
    static constexpr int M2 = 469762049, P2 = 3;
    static constexpr int M3 = 1224736769, P3 = 3;

    auto res1 = number_theoretic_transform<modint<M1>, P1, 1 << 20>().convolve(f, g);
    auto res2 = number_theoretic_transform<modint<M2>, P2, 1 << 20>().convolve(f, g);
    auto res3 = number_theoretic_transform<modint<M3>, P3, 1 << 20>().convolve(f, g);

    const int n = res1.size();

    std::vector<T> ret(n);

    const int64_t M12 = (int64_t)modint<M2>::inv(M1);
    const int64_t M13 = (int64_t)modint<M3>::inv(M1);
    const int64_t M23 = (int64_t)modint<M3>::inv(M2);

    for(int i = 0; i < n; ++i){
      const int64_t r[3] = {(int64_t)res1[i], (int64_t)res2[i], (int64_t)res3[i]};

      const int64_t t0 = r[0] % M1;
      const int64_t t1 = (r[1] - t0 + M2) * M12 % M2;
      const int64_t t2 = ((r[2] - t0 + M3) * M13 % M3 - t1 + M3) * M23 % M3;

      ret[i] = T(t0) + T(t1) * M1 + T(t2) * M1 * M2;
    }

    return ret;
  }
}
#line 3 "/home/haar/Downloads/kyopro-lib/Mylib/Number/Mod/mod_pow.cpp"

namespace haar_lib {
  constexpr int64_t mod_pow(int64_t n, int64_t p, int64_t m){
    int64_t ret = 1;
    while(p > 0){
      if(p & 1) (ret *= n) %= m;
      (n *= n) %= m;
      p >>= 1;
    }
    return ret;
  }
}
#line 3 "/home/haar/Downloads/kyopro-lib/Mylib/Number/Prime/primitive_root.cpp"

namespace haar_lib {
  constexpr int primitive_root(int p){
    int pf[30] = {};
    int k = 0;
    {
      int n = p - 1;
      for(int64_t i = 2; i * i <= p; ++i){
        if(n % i == 0){
          pf[k++] = i;
          while(n % i == 0) n /= i;
        }
      }
      if(n != 1)
        pf[k++] = n;
    }

    for(int g = 2; g <= p; ++g){
      bool ok = true;
      for(int i = 0; i < k; ++i){
        if(mod_pow(g, (p - 1) / pf[i], p) == 1){
          ok = false;
          break;
        }
      }

      if(not ok) continue;

      return g;
    }
    return -1;
  }
}
#line 5 "/home/haar/Downloads/kyopro-lib/Mylib/IO/join.cpp"

namespace haar_lib {
  template <typename Iter>
  std::string join(Iter first, Iter last, std::string delim = " "){
    std::stringstream s;

    for(auto it = first; it != last; ++it){
      if(it != first) s << delim;
      s << *it;
    }

    return s.str();
  }
}
#line 8 "main.cpp"


#ifdef DEBUG
#include <Mylib/Debug/debug.cpp>
#else
#define dump(...)
#endif

using namespace haar_lib;


namespace haar_lib {
  template <typename T, const auto &convolve>
  auto convolution_multiply(const std::vector<T> &A, const std::vector<T> &B, int P){
    const int p_root = primitive_root(P);

    std::vector<int> index(P);

    {
      int64_t s = 1;

      for(int i = 0; i < P; ++i){
        index[s] = i;
        s *= p_root;
        if(s >= P) s %= P;
      }
    }

    std::vector<T> a(P), b(P);
    for(int i = 0; i < (int)A.size(); ++i) a[index[i % P]] = A[i];
    for(int i = 0; i < (int)B.size(); ++i) b[index[i % P]] = B[i];

    auto c = convolve(a, b);
    std::vector<T> ret(P);

    {
      int64_t s = 1;

      for(auto x : c){
        ret[s] += x;
        s *= p_root;
        if(s >= P) s %= P;
      }
    }

    return ret;
  }
};


constexpr int mod = 998244353;
constexpr int prim_root = primitive_root(mod);
using mint = modint<mod>;
using NTT = number_theoretic_transform<mint, prim_root, 1 << 20>;
const static auto ntt = NTT();

int main(){
  std::cin.tie(0);
  std::ios::sync_with_stdio(false);

  int P; std::cin >> P;
  std::vector<mint> A(P), B(P);
  for(int i = 1; i < P; ++i) std::cin >> A[i];
  for(int i = 1; i < P; ++i) std::cin >> B[i];

  std::vector<mint> ans = convolution_multiply<mint, ntt>(A, B, P);

  std::cout << join(ans.begin() + 1, ans.end()) << "\n";

  return 0;
}
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