結果

問題 No.1889 K Consecutive Ks (Hard)
ユーザー 👑 emthrmemthrm
提出日時 2022-03-27 04:53:24
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 1,179 ms / 6,000 ms
コード長 9,925 bytes
コンパイル時間 2,954 ms
コンパイル使用メモリ 215,864 KB
実行使用メモリ 18,400 KB
最終ジャッジ日時 2024-04-23 18:56:40
合計ジャッジ時間 18,510 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
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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
6,812 KB
testcase_01 AC 2 ms
6,944 KB
testcase_02 AC 1,178 ms
18,276 KB
testcase_03 AC 2 ms
6,944 KB
testcase_04 AC 2 ms
6,940 KB
testcase_05 AC 2 ms
6,944 KB
testcase_06 AC 2 ms
6,940 KB
testcase_07 AC 1 ms
6,940 KB
testcase_08 AC 2 ms
6,940 KB
testcase_09 AC 1,165 ms
17,948 KB
testcase_10 AC 1,176 ms
18,128 KB
testcase_11 AC 253 ms
7,260 KB
testcase_12 AC 537 ms
10,848 KB
testcase_13 AC 266 ms
7,616 KB
testcase_14 AC 545 ms
10,840 KB
testcase_15 AC 571 ms
11,696 KB
testcase_16 AC 1,170 ms
18,008 KB
testcase_17 AC 255 ms
7,296 KB
testcase_18 AC 1,137 ms
17,728 KB
testcase_19 AC 1,169 ms
18,032 KB
testcase_20 AC 1,173 ms
18,400 KB
testcase_21 AC 1,176 ms
18,148 KB
testcase_22 AC 1,179 ms
18,208 KB
testcase_23 AC 564 ms
11,384 KB
testcase_24 AC 1,176 ms
18,148 KB
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ソースコード

diff # 

#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 = 998244353;
constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1};
constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1};
constexpr int 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 M>
struct MInt {
  unsigned int v;
  MInt() : v(0) {}
  MInt(const long long x) : v(x >= 0 ? x % M : x % M + M) {}
  static constexpr int get_mod() { return M; }
  static void set_mod(const int divisor) { assert(divisor == M); }
  static void init(const int x = 10000000) {
    inv(x, true);
    fact(x);
    fact_inv(x);
  }
  static MInt inv(const int n, const bool init = false) {
    // assert(0 <= n && n < M && std::__gcd(n, M) == 1);
    static std::vector<MInt> inverse{0, 1};
    const int prev = inverse.size();
    if (n < prev) {
      return inverse[n];
    } else if (init) {
      // "n!" and "M" must be disjoint.
      inverse.resize(n + 1);
      for (int i = prev; i <= n; ++i) {
        inverse[i] = -inverse[M % i] * (M / i);
      }
      return inverse[n];
    }
    int u = 1, v = 0;
    for (unsigned int a = n, b = M; b;) {
      const unsigned int q = a / b;
      std::swap(a -= q * b, b);
      std::swap(u -= q * v, v);
    }
    return u;
  }
  static MInt fact(const int n) {
    static std::vector<MInt> factorial{1};
    const int prev = factorial.size();
    if (n >= prev) {
      factorial.resize(n + 1);
      for (int i = prev; i <= n; ++i) {
        factorial[i] = factorial[i - 1] * i;
      }
    }
    return factorial[n];
  }
  static MInt fact_inv(const int n) {
    static std::vector<MInt> f_inv{1};
    const int prev = f_inv.size();
    if (n >= prev) {
      f_inv.resize(n + 1);
      f_inv[n] = inv(fact(n).v);
      for (int i = n; i > prev; --i) {
        f_inv[i - 1] = f_inv[i] * i;
      }
    }
    return f_inv[n];
  }
  static MInt nCk(const int n, const int k) {
    if (n < 0 || n < k || k < 0) return 0;
    return fact(n) * (n - k < k ? fact_inv(k) * fact_inv(n - k) :
                                  fact_inv(n - k) * fact_inv(k));
  }
  static MInt nPk(const int n, const int k) {
    return n < 0 || n < k || k < 0 ? 0 : fact(n) * fact_inv(n - k);
  }
  static MInt nHk(const int n, const int k) {
    return n < 0 || k < 0 ? 0 : (k == 0 ? 1 : nCk(n + k - 1, k));
  }
  static MInt large_nCk(long long n, const int k) {
    if (n < 0 || n < k || k < 0) return 0;
    inv(k, true);
    MInt res = 1;
    for (int i = 1; i <= k; ++i) {
      res *= inv(i) * n--;
    }
    return res;
  }
  MInt pow(long long exponent) const {
    MInt res = 1, tmp = *this;
    for (; exponent > 0; exponent >>= 1) {
      if (exponent & 1) res *= tmp;
      tmp *= tmp;
    }
    return res;
  }
  MInt& operator+=(const MInt& x) {
    if ((v += x.v) >= M) v -= M;
    return *this;
  }
  MInt& operator-=(const MInt& x) {
    if ((v += M - x.v) >= M) v -= M;
    return *this;
  }
  MInt& operator*=(const MInt& x) {
    v = static_cast<unsigned long long>(v) * x.v % M;
    return *this;
  }
  MInt& operator/=(const MInt& x) { return *this *= inv(x.v); }
  bool operator==(const MInt& x) const { return v == x.v; }
  bool operator!=(const MInt& x) const { return v != x.v; }
  bool operator<(const MInt& x) const { return v < x.v; }
  bool operator<=(const MInt& x) const { return v <= x.v; }
  bool operator>(const MInt& x) const { return v > x.v; }
  bool operator>=(const MInt& x) const { return v >= x.v; }
  MInt& operator++() {
    if (++v == M) v = 0;
    return *this;
  }
  MInt operator++(int) {
    const MInt res = *this;
    ++*this;
    return res;
  }
  MInt& operator--() {
    v = (v == 0 ? M - 1 : v - 1);
    return *this;
  }
  MInt operator--(int) {
    const MInt res = *this;
    --*this;
    return res;
  }
  MInt operator+() const { return *this; }
  MInt operator-() const { return MInt(v ? M - v : 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.v;
  }
  friend std::istream& operator>>(std::istream& is, MInt& x) {
    long long v;
    is >> v;
    x = MInt(v);
    return is;
  }
};
using ModInt = MInt<MOD>;

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

  NumberTheoreticTransform() {
    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((primes[i][0] - 1) >> primes[i][2]);
        return;
      }
    }
    assert(false);
  }

  template <typename U>
  std::vector<ModInt> dft(const std::vector<U>& a) {
    const int n = a.size();
    int lg = 1;
    while ((1 << lg) < n) ++lg;
    std::vector<ModInt> b(1 << lg, 0);
    std::copy(a.begin(), a.end(), b.begin());
    calc(&b);
    return b;
  }

  void idft(std::vector<ModInt>* a) {
    const int n = a->size();
    assert(__builtin_popcount(n) == 1);
    calc(a);
    std::reverse(std::next(a->begin()), a->end());
    const 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) {
    const int a_size = a.size(), b_size = b.size();
    const int c_size = a_size + b_size - 1;
    int lg = 1;
    while ((1 << lg) < c_size) ++lg;
    const int n = 1 << lg;
    std::vector<ModInt> c(n, 0), d(n, 0);
    std::copy(a.begin(), a.end(), c.begin());
    calc(&c);
    std::copy(b.begin(), b.end(), d.begin());
    calc(&d);
    for (int i = 0; i < n; ++i) {
      c[i] *= d[i];
    }
    idft(&c);
    c.resize(c_size);
    return c;
  }

 private:
  const 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(std::vector<ModInt>* a) {
    const int n = a->size(), prev_n = butterfly.size();
    if (n > prev_n) {
      assert(n <= n_max);
      butterfly.resize(n);
      const 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);
        const ModInt tmp = root.pow((ModInt::get_mod() - 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;
        }
      }
    }
    const int shift = __builtin_ctz(butterfly.size()) - __builtin_ctz(n);
    for (int i = 0; i < n; ++i) {
      const int j = butterfly[i] >> shift;
      if (i < j) std::swap((*a)[i], (*a)[j]);
    }
    for (int block = 1, den = 0; block < n; block <<= 1, ++den) {
      for (int i = 0; i < n; i += (block << 1)) {
        for (int j = 0; j < block; ++j) {
          const ModInt tmp = (*a)[i + j + block] * omega[den][j];
          (*a)[i + j + block] = (*a)[i + j] - tmp;
          (*a)[i + j] += tmp;
        }
      }
    }
  }
};

void convert_online_dp_to_offline_dp(
    const int n, const std::function<void(int, int, int)> induce) {
  const std::function<void(const int, const int)> solve =
      [induce, &solve](const int l, const int r) -> void {
        if (l + 1 == r) {
          // dp(l) <- dp(l) ･ b_l
          return;
        }
        const int m = (l + r) >> 1;
        solve(l, m);
        induce(l, m, r);
        solve(m, r);
      };
  if (n > 0) solve(0, n);
}

int main() {
  int n, m; cin >> n >> m;
  NumberTheoreticTransform<MOD> ntt;
  vector<ModInt> d(n + 1, 0), p(n, 1);
  for (int i = 1; i <= n && i <= m; ++i) {
    for (int j = i; j <= n; j += i) ++d[j];
  }
  if (n >= 2) p[1] = m - 1;
  FOR(i, 2, n) p[i] = p[i - 1] * m;
  vector<ModInt> dp(n + 1, 0), dp2(n + 1, 1);
  REP(i, n) dp2[i + 1] = dp2[i] * m;
  const function<void(int, int, int)> induce = [&](int l, int m, int r) -> void {
    const vector<ModInt> tmp = ntt.convolution(vector(dp2.begin() + l, dp2.begin() + m), vector(d.begin(), d.begin() + (r - l)));
    FOR(i, m, r) {
      dp[i] += tmp[i - l];
      dp2[i] -= tmp[i - l];
    }
    const vector<ModInt> tmp2 = ntt.convolution(vector(dp.begin() + l, dp.begin() + m), vector(p.begin(), p.begin() + (r - l)));
    FOR(i, m, r) dp2[i] -= tmp2[i - l];
  };
  convert_online_dp_to_offline_dp(n + 1, induce);
  cout << ModInt(m).pow(n) - dp2[n] << '\n';
  return 0;
}
0