#919710 (C++14) No.2506 Sum of Weighted Powers

• 問題: No.2506 Sum of Weighted Powers
• ユーザー: 👑 hos.lyric
• 提出日時: 2023-10-13 21:25:45
• 言語: C++14 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 434 ms / 2,000 ms
• コード長: 10,932 bytes
• コンパイル時間: 1,415 ms
• コンパイル使用メモリ: 119,048 KB
• 実行使用メモリ: 24,192 KB
• 最終ジャッジ日時: 2024-09-15 17:00:32
• 合計ジャッジ時間: 6,674 ms
• ジャッジサーバーID （参考情報）: judge6 / judge4

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	3 ms; 5,376 KB
testcase_04	AC	2 ms; 5,376 KB
testcase_05	AC	2 ms; 5,376 KB
testcase_06	AC	4 ms; 5,376 KB
testcase_07	AC	3 ms; 5,376 KB
testcase_08	AC	5 ms; 5,376 KB
testcase_09	AC	4 ms; 5,376 KB
testcase_10	AC	5 ms; 5,376 KB
testcase_11	AC	5 ms; 5,376 KB
testcase_12	AC	2 ms; 5,376 KB
testcase_13	AC	2 ms; 5,376 KB
testcase_14	AC	2 ms; 5,376 KB
testcase_15	AC	2 ms; 5,376 KB
testcase_16	AC	2 ms; 5,376 KB
testcase_17	AC	3 ms; 5,376 KB
testcase_18	AC	4 ms; 5,376 KB
testcase_19	AC	2 ms; 5,376 KB
testcase_20	AC	3 ms; 5,376 KB
testcase_21	AC	5 ms; 5,376 KB
testcase_22	AC	4 ms; 5,376 KB
testcase_23	AC	252 ms; 14,080 KB
testcase_24	AC	347 ms; 23,424 KB
testcase_25	AC	104 ms; 8,576 KB
testcase_26	AC	381 ms; 23,808 KB
testcase_27	AC	39 ms; 5,888 KB
testcase_28	AC	431 ms; 24,192 KB
testcase_29	AC	432 ms; 24,064 KB
testcase_30	AC	409 ms; 24,192 KB
testcase_31	AC	428 ms; 24,192 KB
testcase_32	AC	434 ms; 24,064 KB
testcase_33	AC	2 ms; 5,376 KB
testcase_34	AC	2 ms; 5,376 KB
testcase_35	AC	54 ms; 5,376 KB
testcase_36	AC	64 ms; 5,376 KB
testcase_37	AC	2 ms; 5,376 KB
testcase_38	AC	2 ms; 5,376 KB
testcase_39	AC	2 ms; 5,376 KB
testcase_40	AC	2 ms; 5,376 KB
testcase_41	AC	2 ms; 5,376 KB

ソースコード

#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")

////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
  static constexpr unsigned M = M_;
  unsigned x;
  constexpr ModInt() : x(0U) {}
  constexpr ModInt(unsigned x_) : x(x_ % M) {}
  constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
  constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
  constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
  ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
  ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
  ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
  ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
  ModInt pow(long long e) const {
    if (e < 0) return inv().pow(-e);
    ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
  }
  ModInt inv() const {
    unsigned a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
    assert(a == 1U); return ModInt(y);
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
  ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
  ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
  ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
  ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
  template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
  template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
  template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
  template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
  explicit operator bool() const { return x; }
  bool operator==(const ModInt &a) const { return (x == a.x); }
  bool operator!=(const ModInt &a) const { return (x != a.x); }
  friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////

constexpr unsigned MO = 943718401;
using Mint = ModInt<MO>;


////////////////////////////////////////////////////////////////////////////////
// M: prime, G: primitive root, 2^K | M - 1
template <unsigned M_, unsigned G_, int K_> struct Fft {
  static_assert(2U <= M_, "Fft: 2 <= M must hold.");
  static_assert(M_ < 1U << 30, "Fft: M < 2^30 must hold.");
  static_assert(1 <= K_, "Fft: 1 <= K must hold.");
  static_assert(K_ < 30, "Fft: K < 30 must hold.");
  static_assert(!((M_ - 1U) & ((1U << K_) - 1U)), "Fft: 2^K | M - 1 must hold.");
  static constexpr unsigned M = M_;
  static constexpr unsigned M2 = 2U * M_;
  static constexpr unsigned G = G_;
  static constexpr int K = K_;
  ModInt<M> FFT_ROOTS[K + 1], INV_FFT_ROOTS[K + 1];
  ModInt<M> FFT_RATIOS[K], INV_FFT_RATIOS[K];
  Fft() {
    const ModInt<M> g(G);
    for (int k = 0; k <= K; ++k) {
      FFT_ROOTS[k] = g.pow((M - 1U) >> k);
      INV_FFT_ROOTS[k] = FFT_ROOTS[k].inv();
    }
    for (int k = 0; k <= K - 2; ++k) {
      FFT_RATIOS[k] = -g.pow(3U * ((M - 1U) >> (k + 2)));
      INV_FFT_RATIOS[k] = FFT_RATIOS[k].inv();
    }
    assert(FFT_ROOTS[1] == M - 1U);
  }
  // as[rev(i)] <- \sum_j \zeta^(ij) as[j]
  void fft(ModInt<M> *as, int n) const {
    assert(!(n & (n - 1))); assert(1 <= n); assert(n <= 1 << K);
    int m = n;
    if (m >>= 1) {
      for (int i = 0; i < m; ++i) {
        const unsigned x = as[i + m].x;  // < M
        as[i + m].x = as[i].x + M - x;  // < 2 M
        as[i].x += x;  // < 2 M
      }
    }
    if (m >>= 1) {
      ModInt<M> prod = 1U;
      for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
        for (int i = i0; i < i0 + m; ++i) {
          const unsigned x = (prod * as[i + m]).x;  // < M
          as[i + m].x = as[i].x + M - x;  // < 3 M
          as[i].x += x;  // < 3 M
        }
        prod *= FFT_RATIOS[__builtin_ctz(++h)];
      }
    }
    for (; m; ) {
      if (m >>= 1) {
        ModInt<M> prod = 1U;
        for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
          for (int i = i0; i < i0 + m; ++i) {
            const unsigned x = (prod * as[i + m]).x;  // < M
            as[i + m].x = as[i].x + M - x;  // < 4 M
            as[i].x += x;  // < 4 M
          }
          prod *= FFT_RATIOS[__builtin_ctz(++h)];
        }
      }
      if (m >>= 1) {
        ModInt<M> prod = 1U;
        for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
          for (int i = i0; i < i0 + m; ++i) {
            const unsigned x = (prod * as[i + m]).x;  // < M
            as[i].x = (as[i].x >= M2) ? (as[i].x - M2) : as[i].x;  // < 2 M
            as[i + m].x = as[i].x + M - x;  // < 3 M
            as[i].x += x;  // < 3 M
          }
          prod *= FFT_RATIOS[__builtin_ctz(++h)];
        }
      }
    }
    for (int i = 0; i < n; ++i) {
      as[i].x = (as[i].x >= M2) ? (as[i].x - M2) : as[i].x;  // < 2 M
      as[i].x = (as[i].x >= M) ? (as[i].x - M) : as[i].x;  // < M
    }
  }
  // as[i] <- (1/n) \sum_j \zeta^(-ij) as[rev(j)]
  void invFft(ModInt<M> *as, int n) const {
    assert(!(n & (n - 1))); assert(1 <= n); assert(n <= 1 << K);
    int m = 1;
    if (m < n >> 1) {
      ModInt<M> prod = 1U;
      for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
        for (int i = i0; i < i0 + m; ++i) {
          const unsigned long long y = as[i].x + M - as[i + m].x;  // < 2 M
          as[i].x += as[i + m].x;  // < 2 M
          as[i + m].x = (prod.x * y) % M;  // < M
        }
        prod *= INV_FFT_RATIOS[__builtin_ctz(++h)];
      }
      m <<= 1;
    }
    for (; m < n >> 1; m <<= 1) {
      ModInt<M> prod = 1U;
      for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
        for (int i = i0; i < i0 + (m >> 1); ++i) {
          const unsigned long long y = as[i].x + M2 - as[i + m].x;  // < 4 M
          as[i].x += as[i + m].x;  // < 4 M
          as[i].x = (as[i].x >= M2) ? (as[i].x - M2) : as[i].x;  // < 2 M
          as[i + m].x = (prod.x * y) % M;  // < M
        }
        for (int i = i0 + (m >> 1); i < i0 + m; ++i) {
          const unsigned long long y = as[i].x + M - as[i + m].x;  // < 2 M
          as[i].x += as[i + m].x;  // < 2 M
          as[i + m].x = (prod.x * y) % M;  // < M
        }
        prod *= INV_FFT_RATIOS[__builtin_ctz(++h)];
      }
    }
    if (m < n) {
      for (int i = 0; i < m; ++i) {
        const unsigned y = as[i].x + M2 - as[i + m].x;  // < 4 M
        as[i].x += as[i + m].x;  // < 4 M
        as[i + m].x = y;  // < 4 M
      }
    }
    const ModInt<M> invN = ModInt<M>(n).inv();
    for (int i = 0; i < n; ++i) {
      as[i] *= invN;
    }
  }
  void fft(vector<ModInt<M>> &as) const {
    fft(as.data(), as.size());
  }
  void invFft(vector<ModInt<M>> &as) const {
    invFft(as.data(), as.size());
  }
  vector<ModInt<M>> convolve(vector<ModInt<M>> as, vector<ModInt<M>> bs) const {
    if (as.empty() || bs.empty()) return {};
    const int len = as.size() + bs.size() - 1;
    int n = 1;
    for (; n < len; n <<= 1) {}
    as.resize(n); fft(as);
    bs.resize(n); fft(bs);
    for (int i = 0; i < n; ++i) as[i] *= bs[i];
    invFft(as);
    as.resize(len);
    return as;
  }
  vector<ModInt<M>> square(vector<ModInt<M>> as) const {
    if (as.empty()) return {};
    const int len = as.size() + as.size() - 1;
    int n = 1;
    for (; n < len; n <<= 1) {}
    as.resize(n); fft(as);
    for (int i = 0; i < n; ++i) as[i] *= as[i];
    invFft(as);
    as.resize(len);
    return as;
  }
};

const Fft<MO, 7, 22> FFT;


int N;
Mint X;
vector<Mint> A[3];

int main() {
  for (; ~scanf("%d%u", &N, &X.x); ) {
    for (int h = 0; h < 3; ++h) {
      A[h].resize(N + 1);
      for (int i = 0; i <= N; ++i) {
        scanf("%u", &A[h][i].x);
      }
    }
    
    Mint ans = 0;
    if (X) {
      int len = 1;
      for (; len < 2 * N + 1; len <<= 1) {}
      vector<Mint> bss[3][3];
      for (int h = 0; h < 3; ++h) {
        for (int s = 0; s < 3; ++s) {
          bss[h][s].assign(len, 0);
        }
      }
      // *= X^(-i^3/3)
      for (int h = 1; h < 3; ++h) {
        for (int i = 0; i <= N; ++i) {
          const Int i3 = -1LL * i * i * i;
          const Int r = (i3 % 3 + 3) % 3;
          const Int q = (i3 - r) / 3;
          bss[h][r][i] += X.pow(q) * A[h][i];
        }
        for (int s = 0; s < 3; ++s) {
          FFT.fft(bss[h][s]);
        }
      }
      for (int i = 0; i < len; ++i) {
        Mint tmp[5] = {};
        for (int s = 0; s < 3; ++s) for (int t = 0; t < 3; ++t) {
          tmp[s + t] += bss[1][s][i] * bss[2][t][i];
        }
        for (int s = 5; --s >= 3; ) {
          tmp[s - 3] += X * tmp[s];
        }
        for (int s = 0; s < 3; ++s) {
          bss[0][s][i] = tmp[s];
        }
      }
      for (int s = 0; s < 3; ++s) {
        FFT.invFft(bss[0][s]);
      }
// for(int s=0;s<3;++s)cerr<<bss[0][s]<<endl;
      // *= X^(i^3/3)
      for (int i = 0; i <= N; ++i) {
        const Int i3 = 1LL * i * i * i;
        const Int q = (i3 + 3 - 1) / 3;
        const Int r = 3 * q - i3;
        ans += A[0][i] * X.pow(q) * bss[0][r][i];
      }
    } else {
      ans += A[0][0] * A[1][0] * A[2][0];
      for (int i = 1; i <= N; ++i) {
        ans += A[0][i] * A[1][i] * A[2][0];
        ans += A[0][i] * A[1][0] * A[2][i];
      }
    }
    printf("%u\n", ans.x);
  }
  return 0;
}