#748881 (C++17) No.1889 K Consecutive Ks (Hard)

提出ソース
結果

問題	No.1889 K Consecutive Ks (Hard)
ユーザー	noshi91
提出日時	2022-03-25 23:18:20
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	88 ms / 6,000 ms
コード長	21,805 bytes
コンパイル時間	2,486 ms
コンパイル使用メモリ	207,708 KB
実行使用メモリ	9,052 KB
最終ジャッジ日時	2024-04-22 08:13:59
合計ジャッジ時間	4,472 ms
ジャッジサーバーID （参考情報）	judge5 / judge1
このコードへのチャレンジ
（要ログイン）
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 6,816 KB
testcase_02	AC	88 ms 8,960 KB
testcase_03	AC	2 ms 6,940 KB
testcase_04	AC	2 ms 6,940 KB
testcase_05	AC	2 ms 6,940 KB
testcase_06	AC	1 ms 6,944 KB
testcase_07	AC	2 ms 6,948 KB
testcase_08	AC	2 ms 6,940 KB
testcase_09	AC	81 ms 8,900 KB
testcase_10	AC	81 ms 8,956 KB
testcase_11	AC	22 ms 6,940 KB
testcase_12	AC	43 ms 6,940 KB
testcase_13	AC	42 ms 6,940 KB
testcase_14	AC	42 ms 6,944 KB
testcase_15	AC	85 ms 8,660 KB
testcase_16	AC	87 ms 8,916 KB
testcase_17	AC	41 ms 6,940 KB
testcase_18	AC	85 ms 8,952 KB
testcase_19	AC	88 ms 9,052 KB
testcase_20	AC	87 ms 8,968 KB
testcase_21	AC	88 ms 8,960 KB
testcase_22	AC	88 ms 8,968 KB
testcase_23	AC	44 ms 6,940 KB
testcase_24	AC	88 ms 8,964 KB
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

raw source code
#include <algorithm>
#include <iostream>
#include <numeric>
#include <vector>

#include <bits/stdc++.h>

// https://ei1333.github.io/library/test/verify/yosupo-inv-of-formal-power-series.test.cpp
namespace ei1333 {

  using namespace std;

#line 1 "template/template.cpp"

  using namespace std;

  using int64 = long long;
  const int mod = 1e9 + 7;

  const int64 infll = (1LL << 62) - 1;
  const int inf = (1 << 30) - 1;

  struct IoSetup {
    IoSetup() {
      cin.tie(nullptr);
      ios::sync_with_stdio(false);
      cout << fixed << setprecision(10);
      cerr << fixed << setprecision(10);
    }
  } iosetup;

  template <typename T1, typename T2>
  ostream& operator<<(ostream& os, const pair<T1, T2>& p) {
    os << p.first << " " << p.second;
    return os;
  }

  template <typename T1, typename T2>
  istream& operator>>(istream& is, pair<T1, T2>& p) {
    is >> p.first >> p.second;
    return is;
  }

  template <typename T> ostream& operator<<(ostream& os, const vector<T>& v) {
    for (int i = 0; i < (int)v.size(); i++) {
      os << v[i] << (i + 1 != v.size() ? " " : "");
    }
    return os;
  }

  template <typename T> istream& operator>>(istream& is, vector<T>& v) {
    for (T& in : v)
      is >> in;
    return is;
  }

  template <typename T1, typename T2> inline bool chmax(T1& a, T2 b) {
    return a < b && (a = b, true);
  }

  template <typename T1, typename T2> inline bool chmin(T1& a, T2 b) {
    return a > b && (a = b, true);
  }

  template <typename T = int64> vector<T> make_v(size_t a) {
    return vector<T>(a);
  }

  template <typename T, typename... Ts> auto make_v(size_t a, Ts... ts) {
    return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
  }

  template <typename T, typename V>
  typename enable_if<is_class<T>::value == 0>::type fill_v(T& t, const V& v) {
    t = v;
  }

  template <typename T, typename V>
  typename enable_if<is_class<T>::value != 0>::type fill_v(T& t, const V& v) {
    for (auto& e : t)
      fill_v(e, v);
  }

  template <typename F> struct FixPoint : F {
    explicit FixPoint(F&& f) : F(forward<F>(f)) {}

    template <typename... Args> decltype(auto) operator()(Args &&... args) const {
      return F::operator()(*this, forward<Args>(args)...);
    }
  };

  template <typename F> inline decltype(auto) MFP(F&& f) {
    return FixPoint<F>{forward<F>(f)};
  }
#line 4 "test/verify/yosupo-inv-of-formal-power-series.test.cpp"

#line 1 "math/combinatorics/mod-int.cpp"
  template <int mod> struct ModInt {
    int x;

    ModInt() : x(0) {}

    ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

    ModInt& operator+=(const ModInt& p) {
      if ((x += p.x) >= mod)
        x -= mod;
      return *this;
    }

    ModInt& operator-=(const ModInt& p) {
      if ((x += mod - p.x) >= mod)
        x -= mod;
      return *this;
    }

    ModInt& operator*=(const ModInt& p) {
      x = (int)(1LL * x * p.x % mod);
      return *this;
    }

    ModInt& operator/=(const ModInt& p) {
      *this *= p.inverse();
      return *this;
    }

    ModInt operator-() const { return ModInt(-x); }

    ModInt operator+(const ModInt& p) const { return ModInt(*this) += p; }

    ModInt operator-(const ModInt& p) const { return ModInt(*this) -= p; }

    ModInt operator*(const ModInt& p) const { return ModInt(*this) *= p; }

    ModInt operator/(const ModInt& p) const { return ModInt(*this) /= p; }

    bool operator==(const ModInt& p) const { return x == p.x; }

    bool operator!=(const ModInt& p) const { return x != p.x; }

    ModInt inverse() const {
      int a = x, b = mod, u = 1, v = 0, t;
      while (b > 0) {
        t = a / b;
        swap(a -= t * b, b);
        swap(u -= t * v, v);
      }
      return ModInt(u);
    }

    ModInt pow(int64_t n) const {
      ModInt ret(1), mul(x);
      while (n > 0) {
        if (n & 1)
          ret *= mul;
        mul *= mul;
        n >>= 1;
      }
      return ret;
    }

    friend ostream& operator<<(ostream& os, const ModInt& p) { return os << p.x; }

    friend istream& operator>>(istream& is, ModInt& a) {
      int64_t t;
      is >> t;
      a = ModInt<mod>(t);
      return (is);
    }

    static int get_mod() { return mod; }
  };

  using modint = ModInt<mod>;
#line 1 "math/fft/number-theoretic-transform-friendly-mod-int.cpp"
  /**
   * @brief Number Theoretic Transform Friendly ModInt
   */
  template <typename Mint> struct NumberTheoreticTransformFriendlyModInt {

    static vector<Mint> roots, iroots, rate3, irate3;
    static int max_base;

    NumberTheoreticTransformFriendlyModInt() = default;

    static void init() {
      if (roots.empty()) {
        const unsigned mod = Mint::get_mod();
        assert(mod >= 3 && mod % 2 == 1);
        auto tmp = mod - 1;
        max_base = 0;
        while (tmp % 2 == 0)
          tmp >>= 1, max_base++;
        Mint root = 2;
        while (root.pow((mod - 1) >> 1) == 1) {
          root += 1;
        }
        assert(root.pow(mod - 1) == 1);

        roots.resize(max_base + 1);
        iroots.resize(max_base + 1);
        rate3.resize(max_base + 1);
        irate3.resize(max_base + 1);

        roots[max_base] = root.pow((mod - 1) >> max_base);
        iroots[max_base] = Mint(1) / roots[max_base];
        for (int i = max_base - 1; i >= 0; i--) {
          roots[i] = roots[i + 1] * roots[i + 1];
          iroots[i] = iroots[i + 1] * iroots[i + 1];
        }
        {
          Mint prod = 1, iprod = 1;
          for (int i = 0; i <= max_base - 3; i++) {
            rate3[i] = roots[i + 3] * prod;
            irate3[i] = iroots[i + 3] * iprod;
            prod *= iroots[i + 3];
            iprod *= roots[i + 3];
          }
        }
      }
    }

    static void ntt(vector<Mint>& a) {
      init();
      const int n = (int)a.size();
      assert((n & (n - 1)) == 0);
      int h = __builtin_ctz(n);
      assert(h <= max_base);
      int len = 0;
      Mint imag = roots[2];
      if (h & 1) {
        int p = 1 << (h - 1);
        Mint rot = 1;
        for (int i = 0; i < p; i++) {
          auto r = a[i + p];
          a[i + p] = a[i] - r;
          a[i] += r;
        }
        len++;
      }
      for (; len + 1 < h; len += 2) {
        int p = 1 << (h - len - 2);
        { // s = 0
          for (int i = 0; i < p; i++) {
            auto a0 = a[i];
            auto a1 = a[i + p];
            auto a2 = a[i + 2 * p];
            auto a3 = a[i + 3 * p];
            auto a1na3imag = (a1 - a3) * imag;
            auto a0a2 = a0 + a2;
            auto a1a3 = a1 + a3;
            auto a0na2 = a0 - a2;
            a[i] = a0a2 + a1a3;
            a[i + 1 * p] = a0a2 - a1a3;
            a[i + 2 * p] = a0na2 + a1na3imag;
            a[i + 3 * p] = a0na2 - a1na3imag;
          }
        }
        Mint rot = rate3[0];
        for (int s = 1; s < (1 << len); s++) {
          int offset = s << (h - len);
          Mint rot2 = rot * rot;
          Mint rot3 = rot2 * rot;
          for (int i = 0; i < p; i++) {
            auto a0 = a[i + offset];
            auto a1 = a[i + offset + p] * rot;
            auto a2 = a[i + offset + 2 * p] * rot2;
            auto a3 = a[i + offset + 3 * p] * rot3;
            auto a1na3imag = (a1 - a3) * imag;
            auto a0a2 = a0 + a2;
            auto a1a3 = a1 + a3;
            auto a0na2 = a0 - a2;
            a[i + offset] = a0a2 + a1a3;
            a[i + offset + 1 * p] = a0a2 - a1a3;
            a[i + offset + 2 * p] = a0na2 + a1na3imag;
            a[i + offset + 3 * p] = a0na2 - a1na3imag;
          }
          rot *= rate3[__builtin_ctz(~s)];
        }
      }
    }

    static void intt(vector<Mint>& a, bool f = true) {
      init();
      const int n = (int)a.size();
      assert((n & (n - 1)) == 0);
      int h = __builtin_ctz(n);
      assert(h <= max_base);
      int len = h;
      Mint iimag = iroots[2];
      for (; len > 1; len -= 2) {
        int p = 1 << (h - len);
        { // s = 0
          for (int i = 0; i < p; i++) {
            auto a0 = a[i];
            auto a1 = a[i + 1 * p];
            auto a2 = a[i + 2 * p];
            auto a3 = a[i + 3 * p];
            auto a2na3iimag = (a2 - a3) * iimag;
            auto a0na1 = a0 - a1;
            auto a0a1 = a0 + a1;
            auto a2a3 = a2 + a3;
            a[i] = a0a1 + a2a3;
            a[i + 1 * p] = (a0na1 + a2na3iimag);
            a[i + 2 * p] = (a0a1 - a2a3);
            a[i + 3 * p] = (a0na1 - a2na3iimag);
          }
        }
        Mint irot = irate3[0];
        for (int s = 1; s < (1 << (len - 2)); s++) {
          int offset = s << (h - len + 2);
          Mint irot2 = irot * irot;
          Mint irot3 = irot2 * irot;
          for (int i = 0; i < p; i++) {
            auto a0 = a[i + offset];
            auto a1 = a[i + offset + 1 * p];
            auto a2 = a[i + offset + 2 * p];
            auto a3 = a[i + offset + 3 * p];
            auto a2na3iimag = (a2 - a3) * iimag;
            auto a0na1 = a0 - a1;
            auto a0a1 = a0 + a1;
            auto a2a3 = a2 + a3;
            a[i + offset] = a0a1 + a2a3;
            a[i + offset + 1 * p] = (a0na1 + a2na3iimag) * irot;
            a[i + offset + 2 * p] = (a0a1 - a2a3) * irot2;
            a[i + offset + 3 * p] = (a0na1 - a2na3iimag) * irot3;
          }
          irot *= irate3[__builtin_ctz(~s)];
        }
      }
      if (len >= 1) {
        int p = 1 << (h - 1);
        for (int i = 0; i < p; i++) {
          auto ajp = a[i] - a[i + p];
          a[i] += a[i + p];
          a[i + p] = ajp;
        }
      }
      if (f) {
        Mint inv_sz = Mint(1) / n;
        for (int i = 0; i < n; i++)
          a[i] *= inv_sz;
      }
    }

    static vector<Mint> multiply(vector<Mint> a, vector<Mint> b) {
      int need = a.size() + b.size() - 1;
      int nbase = 1;
      while ((1 << nbase) < need)
        nbase++;
      int sz = 1 << nbase;
      a.resize(sz, 0);
      b.resize(sz, 0);
      ntt(a);
      ntt(b);
      Mint inv_sz = Mint(1) / sz;
      for (int i = 0; i < sz; i++)
        a[i] *= b[i] * inv_sz;
      intt(a, false);
      a.resize(need);
      return a;
    }
  };

  template <typename Mint>
  vector<Mint>
    NumberTheoreticTransformFriendlyModInt<Mint>::roots = vector<Mint>();
  template <typename Mint>
  vector<Mint>
    NumberTheoreticTransformFriendlyModInt<Mint>::iroots = vector<Mint>();
  template <typename Mint>
  vector<Mint>
    NumberTheoreticTransformFriendlyModInt<Mint>::rate3 = vector<Mint>();
  template <typename Mint>
  vector<Mint>
    NumberTheoreticTransformFriendlyModInt<Mint>::irate3 = vector<Mint>();
  template <typename Mint>
  int NumberTheoreticTransformFriendlyModInt<Mint>::max_base = 0;
#line 2 "math/fps/formal-power-series-friendly-ntt.cpp"

  /**
   * @brief Formal Power Series Friendly NTT(NTTmod用形式的冪級数)
   * @docs docs/formal-power-series-friendly-ntt.md
   */
  template <typename T> struct FormalPowerSeriesFriendlyNTT : vector<T> {
    using vector<T>::vector;
    using P = FormalPowerSeriesFriendlyNTT;
    using NTT = NumberTheoreticTransformFriendlyModInt<T>;

    P pre(int deg) const {
      return P(begin(*this), begin(*this) + min((int)this->size(), deg));
    }

    P rev(int deg = -1) const {
      P ret(*this);
      if (deg != -1)
        ret.resize(deg, T(0));
      reverse(begin(ret), end(ret));
      return ret;
    }

    void shrink() {
      while (this->size() && this->back() == T(0))
        this->pop_back();
    }

    P operator+(const P& r) const { return P(*this) += r; }

    P operator+(const T& v) const { return P(*this) += v; }

    P operator-(const P& r) const { return P(*this) -= r; }

    P operator-(const T& v) const { return P(*this) -= v; }

    P operator*(const P& r) const { return P(*this) *= r; }

    P operator*(const T& v) const { return P(*this) *= v; }

    P operator/(const P& r) const { return P(*this) /= r; }

    P operator%(const P& r) const { return P(*this) %= r; }

    P& operator+=(const P& r) {
      if (r.size() > this->size())
        this->resize(r.size());
      for (int i = 0; i < (int)r.size(); i++)
        (*this)[i] += r[i];
      return *this;
    }

    P& operator-=(const P& r) {
      if (r.size() > this->size())
        this->resize(r.size());
      for (int i = 0; i < (int)r.size(); i++)
        (*this)[i] -= r[i];
      return *this;
    }

    // https://judge.yosupo.jp/problem/convolution_mod
    P& operator*=(const P& r) {
      if (this->empty() || r.empty()) {
        this->clear();
        return *this;
      }
      auto ret = NTT::multiply(*this, r);
      return *this = { begin(ret), end(ret) };
    }

    P& operator/=(const P& r) {
      if (this->size() < r.size()) {
        this->clear();
        return *this;
      }
      int n = this->size() - r.size() + 1;
      return *this = (rev().pre(n) * r.rev().inv(n)).pre(n).rev(n);
    }

    P& operator%=(const P& r) {
      *this -= *this / r * r;
      shrink();
      return *this;
    }

    // https://judge.yosupo.jp/problem/division_of_polynomials
    pair<P, P> div_mod(const P& r) {
      P q = *this / r;
      P x = *this - q * r;
      x.shrink();
      return make_pair(q, x);
    }

    P operator-() const {
      P ret(this->size());
      for (int i = 0; i < (int)this->size(); i++)
        ret[i] = -(*this)[i];
      return ret;
    }

    P& operator+=(const T& r) {
      if (this->empty())
        this->resize(1);
      (*this)[0] += r;
      return *this;
    }

    P& operator-=(const T& r) {
      if (this->empty())
        this->resize(1);
      (*this)[0] -= r;
      return *this;
    }

    P& operator*=(const T& v) {
      for (int i = 0; i < (int)this->size(); i++)
        (*this)[i] *= v;
      return *this;
    }

    P dot(P r) const {
      P ret(min(this->size(), r.size()));
      for (int i = 0; i < (int)ret.size(); i++)
        ret[i] = (*this)[i] * r[i];
      return ret;
    }

    P operator>>(int sz) const {
      if ((int)this->size() <= sz)
        return {};
      P ret(*this);
      ret.erase(ret.begin(), ret.begin() + sz);
      return ret;
    }

    P operator<<(int sz) const {
      P ret(*this);
      ret.insert(ret.begin(), sz, T(0));
      return ret;
    }

    T operator()(T x) const {
      T r = 0, w = 1;
      for (auto& v : *this) {
        r += w * v;
        w *= x;
      }
      return r;
    }

    P diff() const {
      const int n = (int)this->size();
      P ret(max(0, n - 1));
      for (int i = 1; i < n; i++)
        ret[i - 1] = (*this)[i] * T(i);
      return ret;
    }

    P integral() const {
      const int n = (int)this->size();
      P ret(n + 1);
      ret[0] = T(0);
      for (int i = 0; i < n; i++)
        ret[i + 1] = (*this)[i] / T(i + 1);
      return ret;
    }

    // https://judge.yosupo.jp/problem/inv_of_formal_power_series
    // F(0) must not be 0
    P inv(int deg = -1) const {
      assert(((*this)[0]) != T(0));
      const int n = (int)this->size();
      if (deg == -1)
        deg = n;
      P res(deg);
      res[0] = { T(1) / (*this)[0] };
      for (int d = 1; d < deg; d <<= 1) {
        P f(2 * d), g(2 * d);
        for (int j = 0; j < min(n, 2 * d); j++)
          f[j] = (*this)[j];
        for (int j = 0; j < d; j++)
          g[j] = res[j];
        NTT::ntt(f);
        NTT::ntt(g);
        f = f.dot(g);
        NTT::intt(f);
        for (int j = 0; j < d; j++)
          f[j] = 0;
        NTT::ntt(f);
        for (int j = 0; j < 2 * d; j++)
          f[j] *= g[j];
        NTT::intt(f);
        for (int j = d; j < min(2 * d, deg); j++)
          res[j] = -f[j];
      }
      return res;
    }

    // https://judge.yosupo.jp/problem/log_of_formal_power_series
    // F(0) must be 1
    P log(int deg = -1) const {
      assert((*this)[0] == T(1));
      const int n = (int)this->size();
      if (deg == -1)
        deg = n;
      return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
    }

    // https://judge.yosupo.jp/problem/sqrt_of_formal_power_series
    P sqrt(int deg = -1,
      const function<T(T)>& get_sqrt = [](T) { return T(1); }) const {
      const int n = (int)this->size();
      if (deg == -1)
        deg = n;
      if ((*this)[0] == T(0)) {
        for (int i = 1; i < n; i++) {
          if ((*this)[i] != T(0)) {
            if (i & 1)
              return {};
            if (deg - i / 2 <= 0)
              break;
            auto ret = (*this >> i).sqrt(deg - i / 2, get_sqrt);
            if (ret.empty())
              return {};
            ret = ret << (i / 2);
            if ((int)ret.size() < deg)
              ret.resize(deg, T(0));
            return ret;
          }
        }
        return P(deg, 0);
      }
      auto sqr = T(get_sqrt((*this)[0]));
      if (sqr * sqr != (*this)[0])
        return {};
      P ret{ sqr };
      T inv2 = T(1) / T(2);
      for (int i = 1; i < deg; i <<= 1) {
        ret = (ret + pre(i << 1) * ret.inv(i << 1)) * inv2;
      }
      return ret.pre(deg);
    }

    P sqrt(const function<T(T)>& get_sqrt, int deg = -1) const {
      return sqrt(deg, get_sqrt);
    }

    // https://judge.yosupo.jp/problem/exp_of_formal_power_series
    // F(0) must be 0
    P exp(int deg = -1) const {
      if (deg == -1)
        deg = this->size();
      assert((*this)[0] == T(0));

      P inv;
      inv.reserve(deg + 1);
      inv.push_back(T(0));
      inv.push_back(T(1));

      auto inplace_integral = [&](P& F) -> void {
        const int n = (int)F.size();
        auto mod = T::get_mod();
        while ((int)inv.size() <= n) {
          int i = inv.size();
          inv.push_back((-inv[mod % i]) * (mod / i));
        }
        F.insert(begin(F), T(0));
        for (int i = 1; i <= n; i++)
          F[i] *= inv[i];
      };

      auto inplace_diff = [](P& F) -> void {
        if (F.empty())
          return;
        F.erase(begin(F));
        T coeff = 1, one = 1;
        for (int i = 0; i < (int)F.size(); i++) {
          F[i] *= coeff;
          coeff += one;
        }
      };

      P b{ 1, 1 < (int)this->size() ? (*this)[1] : 0 }, c{ 1 }, z1, z2{ 1, 1 };
      for (int m = 2; m < deg; m *= 2) {
        auto y = b;
        y.resize(2 * m);
        NTT::ntt(y);
        z1 = z2;
        P z(m);
        for (int i = 0; i < m; ++i)
          z[i] = y[i] * z1[i];
        NTT::intt(z);
        fill(begin(z), begin(z) + m / 2, T(0));
        NTT::ntt(z);
        for (int i = 0; i < m; ++i)
          z[i] *= -z1[i];
        NTT::intt(z);
        c.insert(end(c), begin(z) + m / 2, end(z));
        z2 = c;
        z2.resize(2 * m);
        NTT::ntt(z2);
        P x(begin(*this), begin(*this) + min<int>(this->size(), m));
        inplace_diff(x);
        x.push_back(T(0));
        NTT::ntt(x);
        for (int i = 0; i < m; ++i)
          x[i] *= y[i];
        NTT::intt(x);
        x -= b.diff();
        x.resize(2 * m);
        for (int i = 0; i < m - 1; ++i)
          x[m + i] = x[i], x[i] = T(0);
        NTT::ntt(x);
        for (int i = 0; i < 2 * m; ++i)
          x[i] *= z2[i];
        NTT::intt(x);
        x.pop_back();
        inplace_integral(x);
        for (int i = m; i < min<int>(this->size(), 2 * m); ++i)
          x[i] += (*this)[i];
        fill(begin(x), begin(x) + m, T(0));
        NTT::ntt(x);
        for (int i = 0; i < 2 * m; ++i)
          x[i] *= y[i];
        NTT::intt(x);
        b.insert(end(b), begin(x) + m, end(x));
      }
      return P{ begin(b), begin(b) + deg };
    }

    // https://judge.yosupo.jp/problem/pow_of_formal_power_series
    P pow(int64_t k, int deg = -1) const {
      const int n = (int)this->size();
      if (deg == -1)
        deg = n;
      for (int i = 0; i < n; i++) {
        if ((*this)[i] != T(0)) {
          T rev = T(1) / (*this)[i];
          P ret = (((*this * rev) >> i).log() * k).exp() * ((*this)[i].pow(k));
          if (i * k > deg)
            return P(deg, T(0));
          ret = (ret << (i * k)).pre(deg);
          if ((int)ret.size() < deg)
            ret.resize(deg, T(0));
          return ret;
        }
      }
      return *this;
    }

    P mod_pow(int64_t k, P g) const {
      P modinv = g.rev().inv();
      auto get_div = [&](P base) {
        if (base.size() < g.size()) {
          base.clear();
          return base;
        }
        int n = base.size() - g.size() + 1;
        return (base.rev().pre(n) * modinv.pre(n)).pre(n).rev(n);
      };
      P x(*this), ret{ 1 };
      while (k > 0) {
        if (k & 1) {
          ret *= x;
          ret -= get_div(ret) * g;
          ret.shrink();
        }
        x *= x;
        x -= get_div(x) * g;
        x.shrink();
        k >>= 1;
      }
      return ret;
    }

    // https://judge.yosupo.jp/problem/polynomial_taylor_shift
    P taylor_shift(T c) const {
      int n = (int)this->size();
      vector<T> fact(n), rfact(n);
      fact[0] = rfact[0] = T(1);
      for (int i = 1; i < n; i++)
        fact[i] = fact[i - 1] * T(i);
      rfact[n - 1] = T(1) / fact[n - 1];
      for (int i = n - 1; i > 1; i--)
        rfact[i - 1] = rfact[i] * T(i);
      P p(*this);
      for (int i = 0; i < n; i++)
        p[i] *= fact[i];
      p = p.rev();
      P bs(n, T(1));
      for (int i = 1; i < n; i++)
        bs[i] = bs[i - 1] * c * rfact[i] * fact[i - 1];
      p = (p * bs).pre(n);
      p = p.rev();
      for (int i = 0; i < n; i++)
        p[i] *= rfact[i];
      return p;
    }
  };

  template <typename Mint> using FPS = FormalPowerSeriesFriendlyNTT<Mint>;
} // namespace ei1333

int main() {
  using Mint = ei1333::ModInt<998244353>;

  int N, M;
  std::cin >> N >> M;

  ei1333::FPS<Mint> p(N + 1);
  p[0] = 1;
  for (int k = 1; k <= M; k++) {
    for (int j = 1; j <= N; j += k) {
      p[j] -= 1;
    }
    for (int j = k; j <= N; j += k) {
      p[j] += 1;
    }
  }

  std::cout << Mint(M).pow(N) - p.inv()[N] << "\n";

  return 0;
}
yukicoder

結果

テストケース

ソースコード
