#718661 (C++14) No.1763 Many Balls

提出ソース

結果

問題	No.1763 Many Balls
ユーザー	👑 hos.lyric
提出日時	2021-11-20 17:45:41
言語	C++14 (gcc 13.2.0 + boost 1.83.0)
結果	AC
実行時間	658 ms / 10,000 ms
コード長	13,867 bytes
コンパイル時間	2,123 ms
コンパイル使用メモリ	133,036 KB
実行使用メモリ	14,756 KB
最終ジャッジ日時	2023-09-02 13:21:45
合計ジャッジ時間	45,108 ms
ジャッジサーバーID （参考情報）	judge11 / judge12

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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	135 ms 11,536 KB
testcase_01	AC	201 ms 11,920 KB
testcase_02	AC	397 ms 12,836 KB
testcase_03	AC	71 ms 10,708 KB
testcase_04	AC	394 ms 13,144 KB
testcase_05	AC	390 ms 12,772 KB
testcase_06	AC	654 ms 14,400 KB
testcase_07	AC	591 ms 14,044 KB
testcase_08	AC	331 ms 12,600 KB
testcase_09	AC	522 ms 13,536 KB
testcase_10	AC	652 ms 14,244 KB
testcase_11	AC	74 ms 10,636 KB
testcase_12	AC	141 ms 11,512 KB
testcase_13	AC	205 ms 11,780 KB
testcase_14	AC	270 ms 12,136 KB
testcase_15	AC	462 ms 13,192 KB
testcase_16	AC	653 ms 14,248 KB
testcase_17	AC	654 ms 14,324 KB
testcase_18	AC	653 ms 14,320 KB
testcase_19	AC	652 ms 14,364 KB
testcase_20	AC	653 ms 14,320 KB
testcase_21	AC	655 ms 14,320 KB
testcase_22	AC	653 ms 14,380 KB
testcase_23	AC	655 ms 14,392 KB
testcase_24	AC	656 ms 14,360 KB
testcase_25	AC	652 ms 14,244 KB
testcase_26	AC	654 ms 14,376 KB
testcase_27	AC	656 ms 14,384 KB
testcase_28	AC	653 ms 14,548 KB
testcase_29	AC	657 ms 14,296 KB
testcase_30	AC	654 ms 14,424 KB
testcase_31	AC	655 ms 14,488 KB
testcase_32	AC	655 ms 14,464 KB
testcase_33	AC	657 ms 14,492 KB
testcase_34	AC	658 ms 14,436 KB
testcase_35	AC	654 ms 14,284 KB
testcase_36	AC	652 ms 14,264 KB
testcase_37	AC	654 ms 14,400 KB
testcase_38	AC	655 ms 14,424 KB
testcase_39	AC	655 ms 14,268 KB
testcase_40	AC	655 ms 14,512 KB
testcase_41	AC	651 ms 14,364 KB
testcase_42	AC	657 ms 14,508 KB
testcase_43	AC	656 ms 14,500 KB
testcase_44	AC	657 ms 14,452 KB
testcase_45	AC	650 ms 14,352 KB
testcase_46	AC	651 ms 14,440 KB
testcase_47	AC	655 ms 14,728 KB
testcase_48	AC	651 ms 14,572 KB
testcase_49	AC	649 ms 14,572 KB
testcase_50	AC	654 ms 14,572 KB
testcase_51	AC	655 ms 14,424 KB
testcase_52	AC	654 ms 14,572 KB
testcase_53	AC	654 ms 14,440 KB
testcase_54	AC	654 ms 14,376 KB
testcase_55	AC	652 ms 14,516 KB
testcase_56	AC	653 ms 14,628 KB
testcase_57	AC	656 ms 14,520 KB
testcase_58	AC	655 ms 14,444 KB
testcase_59	AC	655 ms 14,756 KB
testcase_60	AC	656 ms 14,576 KB
testcase_61	AC	655 ms 14,516 KB
testcase_62	AC	651 ms 14,436 KB
testcase_63	AC	655 ms 14,568 KB
testcase_64	AC	652 ms 14,504 KB
testcase_65	AC	652 ms 14,428 KB

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ソースコード

raw source code

#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 <map>
#include <numeric>
#include <queue>
#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> 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; }


////////////////////////////////////////////////////////////////////////////////
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; }
};
////////////////////////////////////////////////////////////////////////////////

////////////////////////////////////////////////////////////////////////////////
// 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;
  }
};

// M0 M1 M2 = 789204840662082423367925761 (> 7.892 * 10^26, > 2^89)
// M0 M3 M4 M5 M6 = 797766583174034668024539679147517452591562753 (> 7.977 * 10^44, > 2^149)
const Fft<998244353U, 3U, 23> FFT0;
const Fft<897581057U, 3U, 23> FFT1;
const Fft<880803841U, 26U, 23> FFT2;
const Fft<985661441U, 3U, 22> FFT3;
const Fft<943718401U, 7U, 22> FFT4;
const Fft<935329793U, 3U, 22> FFT5;
const Fft<918552577U, 5U, 22> FFT6;

// T = unsigned, unsigned long long, ModInt<M>
template <class T, unsigned M0, unsigned M1, unsigned M2>
T garner(ModInt<M0> a0, ModInt<M1> a1, ModInt<M2> a2) {
  static const ModInt<M1> INV_M0_M1 = ModInt<M1>(M0).inv();
  static const ModInt<M2> INV_M0M1_M2 = (ModInt<M2>(M0) * M1).inv();
  const ModInt<M1> b1 = INV_M0_M1 * (a1 - a0.x);
  const ModInt<M2> b2 = INV_M0M1_M2 * (a2 - (ModInt<M2>(b1.x) * M0 + a0.x));
  return (T(b2.x) * M1 + b1.x) * M0 + a0.x;
}
template <class T, unsigned M0, unsigned M1, unsigned M2, unsigned M3, unsigned M4>
T garner(ModInt<M0> a0, ModInt<M1> a1, ModInt<M2> a2, ModInt<M3> a3, ModInt<M4> a4) {
  static const ModInt<M1> INV_M0_M1 = ModInt<M1>(M0).inv();
  static const ModInt<M2> INV_M0M1_M2 = (ModInt<M2>(M0) * M1).inv();
  static const ModInt<M3> INV_M0M1M2_M3 = (ModInt<M3>(M0) * M1 * M2).inv();
  static const ModInt<M4> INV_M0M1M2M3_M4 = (ModInt<M4>(M0) * M1 * M2 * M3).inv();
  const ModInt<M1> b1 = INV_M0_M1 * (a1 - a0.x);
  const ModInt<M2> b2 = INV_M0M1_M2 * (a2 - (ModInt<M2>(b1.x) * M0 + a0.x));
  const ModInt<M3> b3 = INV_M0M1M2_M3 * (a3 - ((ModInt<M3>(b2.x) * M1 + b1.x) * M0 + a0.x));
  const ModInt<M4> b4 = INV_M0M1M2M3_M4 * (a4 - (((ModInt<M4>(b3.x) * M2 + b2.x) * M1 + b1.x) * M0 + a0.x));
  return (((T(b4.x) * M3 + b3.x) * M2 + b2.x) * M1 + b1.x) * M0 + a0.x;
}

template <unsigned M> vector<ModInt<M>> convolve(const vector<ModInt<M>> &as, const vector<ModInt<M>> &bs) {
  static constexpr unsigned M0 = decltype(FFT0)::M;
  static constexpr unsigned M1 = decltype(FFT1)::M;
  static constexpr unsigned M2 = decltype(FFT2)::M;
  if (as.empty() || bs.empty()) return {};
  const int asLen = as.size(), bsLen = bs.size();
  vector<ModInt<M0>> as0(asLen), bs0(bsLen);
  for (int i = 0; i < asLen; ++i) as0[i] = as[i].x;
  for (int i = 0; i < bsLen; ++i) bs0[i] = bs[i].x;
  const vector<ModInt<M0>> cs0 = FFT0.convolve(as0, bs0);
  vector<ModInt<M1>> as1(asLen), bs1(bsLen);
  for (int i = 0; i < asLen; ++i) as1[i] = as[i].x;
  for (int i = 0; i < bsLen; ++i) bs1[i] = bs[i].x;
  const vector<ModInt<M1>> cs1 = FFT1.convolve(as1, bs1);
  vector<ModInt<M2>> as2(asLen), bs2(bsLen);
  for (int i = 0; i < asLen; ++i) as2[i] = as[i].x;
  for (int i = 0; i < bsLen; ++i) bs2[i] = bs[i].x;
  const vector<ModInt<M2>> cs2 = FFT2.convolve(as2, bs2);
  vector<ModInt<M>> cs(asLen + bsLen - 1);
  for (int i = 0; i < asLen + bsLen - 1; ++i) {
    cs[i] = garner<ModInt<M>>(cs0[i], cs1[i], cs2[i]);
  }
  return cs;
}
template <unsigned M> vector<ModInt<M>> square(const vector<ModInt<M>> &as) {
  static constexpr unsigned M0 = decltype(FFT0)::M;
  static constexpr unsigned M1 = decltype(FFT1)::M;
  static constexpr unsigned M2 = decltype(FFT2)::M;
  if (as.empty()) return {};
  const int asLen = as.size();
  vector<ModInt<M0>> as0(asLen);
  for (int i = 0; i < asLen; ++i) as0[i] = as[i].x;
  const vector<ModInt<M0>> cs0 = FFT0.square(as0);
  vector<ModInt<M1>> as1(asLen);
  for (int i = 0; i < asLen; ++i) as1[i] = as[i].x;
  const vector<ModInt<M1>> cs1 = FFT1.square(as1);
  vector<ModInt<M2>> as2(asLen);
  for (int i = 0; i < asLen; ++i) as2[i] = as[i].x;
  const vector<ModInt<M2>> cs2 = FFT2.square(as2);
  vector<ModInt<M>> cs(asLen + asLen - 1);
  for (int i = 0; i < asLen + asLen - 1; ++i) {
    cs[i] = garner<ModInt<M>>(cs0[i], cs1[i], cs2[i]);
  }
  return cs;
}


constexpr unsigned MO = 90001;
using Mint = ModInt<MO>;

constexpr int L = 60;
const Mint G = Mint(13).pow((MO - 1) / L);

char S[200'010];
int M;
int K[10];
int A[10][10];

int main() {
  for (; ~scanf("%s%d", S, &M); ) {
    for (int i = 0; i < M; ++i) {
      scanf("%d", &K[i]);
      for (int k = 0; k < K[i]; ++k) {
        scanf("%d", &A[i][k]);
      }
    }
    
    vector<vector<Mint>> fss(M);
    for (int i = 0; i < M; ++i) {
      fss[i].assign(MO, 0);
      for (int p = 1; p < 1 << K[i]; ++p) {
        int l = 1;
        for (int k = 0; k < K[i]; ++k) if (p >> k & 1) {
          l = l / __gcd(l, A[i][k]) * A[i][k];
        }
        const Mint coef = -(__builtin_parity(p) ? -1 : +1) * Mint(l).inv();
// cerr<<i<<": "<<l<<" "<<coef<<endl;
        for (int j = 0; j < l; ++j) {
          fss[i][G.pow(L / l * j).x] += coef;
        }
      }
    }
    
    vector<Mint> prod(MO, 0);
    prod[1] = 1;
    for (int i = 0; i < M; ++i) {
      prod = convolve(prod, fss[i]);
      for (int j = MO; j < (int)prod.size(); ++j) {
        prod[j - MO] += prod[j];
      }
      prod.resize(MO);
    }
    
    Int n = 0;
    for (int h = 0; S[h]; ++h) {
      n = n * 10 + (S[h] - '0');
      n = 1 + (n - 1) % (MO - 1);
    }
    Mint ans = 0;
    for (int x = 0; x < (int)MO; ++x) {
      ans += prod[x] * Mint(x).pow(n);
    }
    printf("%u\n", ans.x);
  }
  return 0;
}
// tsurai

yukicoder

結果

テストケース

ソースコード