結果

問題 No.8046 yukicoderの過去問
コンテスト
ユーザー keijak
提出日時 2021-12-27 06:43:02
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
TLE  
実行時間 -
コード長 10,547 bytes
コンパイル時間 3,995 ms
コンパイル使用メモリ 252,536 KB
最終ジャッジ日時 2025-01-27 07:19:33
ジャッジサーバーID
（参考情報） 		judge4 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
other AC * 4 TLE * 5
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

diff # 

#include <bits/stdc++.h>
#define REP_(i, a_, b_, a, b, ...) for (int i = (a), END_##i = (b); i < END_##i; ++i)
#define REP(i, ...) REP_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define ALL(x) std::begin(x), std::end(x)
using Int = long long;
using Uint = unsigned long long;
using Real = long double;

#include <atcoder/convolution>
#include <atcoder/math>
#include <atcoder/modint>
using Mint = atcoder::modint1000000007;
std::ostream &operator<<(std::ostream &os, const Mint &m) {
  return os << m.val();
}

template<typename T, typename U>
inline bool chmax(T &a, U b) {
  return a < b and ((a = std::move(b)), true);
}
template<typename T, typename U>
inline bool chmin(T &a, U b) {
  return a > b and ((a = std::move(b)), true);
}
template<typename T>
inline int ssize(const T &a) {
  return (int) a.size();
}

struct Void {};

template<class T>
inline std::ostream &print_one(const T &x, char endc) {
  if constexpr (std::is_same<T, Void>::value) {
    return std::cout;  // print nothing
  } else if constexpr (std::is_same<T, bool>::value) {
    return std::cout << (x ? "Yes" : "No") << endc;
  } else {
    return std::cout << x << endc;
  }
}
template<class T>
inline std::ostream &print(const T &x) { return print_one(x, '\n'); }
template<typename T, typename... Ts>
std::ostream &print(const T &head, Ts... tail) {
  return print_one(head, ' '), print(tail...);
}
inline std::ostream &print() { return std::cout << '\n'; }

template<typename Container>
std::ostream &print_seq(const Container &seq,
                        const char *sep = " ",
                        const char *ends = "\n",
                        std::ostream &os = std::cout) {
  const auto itl = std::begin(seq), itr = std::end(seq);
  for (auto it = itl; it != itr; ++it) {
    if (it != itl) os << sep;
    os << *it;
  }
  return os << ends;
}

struct CastInput {
  template<typename T>
  operator T() const {
    T x;
    std::cin >> x;
    return x;
  }
  struct Sized {
    std::size_t n;
    template<typename T>
    operator T() const {
      T x(n);
      for (auto &e: x) std::cin >> e;
      return x;
    }
  };
  Sized operator()(std::size_t n) const { return {n}; }
} in;

#ifdef MY_DEBUG
#include "debug_dump.hpp"
#include "backward.hpp"
backward::SignalHandling kSignalHandling;
#else
#define DUMP(...)
#define cerr if(false)cerr
#endif

// T: modint
template<typename T, int DMAX>
struct ArbitraryModMult {
  using value_type = T;
  static_assert(atcoder::internal::is_modint<T>::value);

  static constexpr int dmax() { return DMAX; }

  static std::vector<T> convolution(const std::vector<T> &x,
                                    const std::vector<T> &y, int size_limit) {
    std::vector<int> xv(x.size());
    std::vector<int> yv(y.size());
    for (int i = 0; i < (int) x.size(); ++i) xv[i] = x[i].val();
    for (int i = 0; i < (int) y.size(); ++i) yv[i] = y[i].val();

    constexpr int M1 = 167772161, M2 = 469762049, M3 = 1224736769;
    const auto z1 = atcoder::convolution<M1>(xv, yv);
    const auto z2 = atcoder::convolution<M2>(xv, yv);
    const auto z3 = atcoder::convolution<M3>(xv, yv);

    const Int m1_inv_m2 = atcoder::inv_mod(M1, M2);
    const Int m12_inv_m3 = atcoder::inv_mod(Int(M1) * M2, M3);
    const Int m12 = Int(M1) * M2 % T::mod();
    const int n = std::min<int>(x.size() + y.size() - 1, size_limit);
    std::vector<T> res(n);
    for (int i = 0; i < n; ++i) {
      atcoder::static_modint<M2> v1 = z2[i] - z1[i];
      v1 *= m1_inv_m2;
      const Int w1 = v1.val() * Int(M1);
      atcoder::static_modint<M3> v2 = z3[i] - z1[i] - w1;
      v2 *= m12_inv_m3;
      res[i] = z1[i] + w1 + (v2.val() * m12);
    }
    return res;
  }

  static std::vector<T> multiply(const std::vector<T> &x,
                                 const std::vector<T> &y) {
    return convolution(x, y, dmax() + 1);
  }

  static std::vector<T> invert(const std::vector<T> &x) {
    assert(x[0].val() != 0);  // must be invertible
    const int n = x.size();
    std::vector<T> res(n);
    res[0] = T(1) / x[0];
    for (int i = 1; i < n; i <<= 1) {
      const int m = std::min(2 * i, n);
      std::vector<T> f(2 * i), g(2 * i);
      for (int j = 0; j < m; ++j) f[j] = x[j];
      for (int j = 0; j < i; ++j) g[j] = res[j];
      f = convolution(f, g, 2 * i);
      f.resize(2 * i);
      for (int j = 0; j < i; ++j) f[j] = 0;
      f = convolution(f, g, 2 * i);
      for (int j = i; j < m; ++j) res[j] = -f[j];
    }
    return res;
  }
};

template<typename Mult>
struct DenseFPS {
  using T = typename Mult::value_type;
  static constexpr int dmax() { return Mult::dmax(); }

  // Coefficients of terms from x^0 to x^DMAX.
  std::vector<T> coeff_;

  DenseFPS() : coeff_(1, 0) {}  // zero

  explicit DenseFPS(std::vector<T> c) : coeff_(std::move(c)) {
    while (size() > dmax() + 1) coeff_.pop_back();
    assert(size() > 0);
  }
  DenseFPS(std::initializer_list<T> c) : coeff_(c.begin(), c.end()) {
    while (size() > dmax() + 1) coeff_.pop_back();
    assert(size() > 0);
  }

  // size <= dmax + 1
  inline int size() const { return static_cast<int>(coeff_.size()); }

  // Returns the coefficient of x^k.
  inline T operator[](int k) const { return (k >= size()) ? 0 : coeff_[k]; }

  // Removes trailing zeros.
  void shrink() {
    while (coeff_.size() > 1 and coeff_.back() == T(0)) coeff_.pop_back();
  }

  DenseFPS &operator+=(const T &scalar) {
    coeff_[0] += scalar;
    return *this;
  }
  friend DenseFPS operator+(const DenseFPS &f, const T &scalar) {
    return DenseFPS(f) += scalar;
  }
  DenseFPS &operator+=(const DenseFPS &other) {
    if (size() < other.size()) coeff_.resize(other.size());
    for (int i = 0; i < other.size(); ++i) coeff_[i] += other[i];
    return *this;
  }
  friend DenseFPS operator+(const DenseFPS &f, const DenseFPS &g) {
    return DenseFPS(f) += g;
  }

  DenseFPS &operator-=(const DenseFPS &other) {
    if (size() < other.size()) coeff_.resize(other.size());
    for (int i = 0; i < other.size(); ++i) coeff_[i] -= other[i];
    return *this;
  }
  friend DenseFPS operator-(const DenseFPS &f, const DenseFPS &g) {
    return DenseFPS(f) -= g;
  }

  DenseFPS operator-() const { return *this * -1; }

  DenseFPS &operator*=(const T &scalar) {
    for (auto &x: coeff_) x *= scalar;
    return *this;
  }
  friend DenseFPS operator*(const DenseFPS &f, const T &scalar) {
    return DenseFPS(f) *= scalar;
  }
  friend DenseFPS operator*(const T &scalar, const DenseFPS &g) {
    return DenseFPS{scalar} *= g;
  }
  DenseFPS &operator*=(const DenseFPS &other) {
    return *this =
               DenseFPS(Mult::multiply(std::move(this->coeff_), other.coeff_));
  }
  friend DenseFPS operator*(const DenseFPS &f, const DenseFPS &g) {
    return DenseFPS(Mult::multiply(f.coeff_, g.coeff_));
  }

  // Multiplies by x^k (with truncation).
  void shift_inplace(int k) {
    if (k > 0) {
      if (size() <= dmax()) {
        coeff_.resize(std::min(size() + k, dmax() + 1), 0);
      }
      for (int i = size() - 1; i >= k; --i) {
        coeff_[i] = coeff_[i - k];
      }
      for (int i = k - 1; i >= 0; --i) {
        coeff_[i] = 0;
      }
    } else if (k < 0) {
      // If coefficients of degrees higher than dmax() were truncated
      // beforehand, you lose the information. Ensure dmax() is big enough.
      coeff_.erase(coeff_.begin(), coeff_.begin() + std::min(-k, size()));
    }
  }
  // Multiplies by x^k.
  DenseFPS shift(int k) const {
    DenseFPS res = *this;
    res.shift_inplace(k);
    return res;
  }

  DenseFPS &operator/=(const T &scalar) {
    for (auto &x: coeff_) x /= scalar;
    return *this;
  }
  friend DenseFPS operator/(const DenseFPS &f, const T &scalar) {
    return DenseFPS(f) /= scalar;
  }
  friend DenseFPS operator/(const T &scalar, const DenseFPS &g) {
    return DenseFPS{scalar} /= g;
  }
  DenseFPS &operator/=(const DenseFPS &other) {
    int z = 0;
    const int msz = std::min(size(), other.size());
    while (z < msz and (*this)[z] == T(0) and other[z] == T(0)) ++z;
    if (z == size()) {
      return *this;  // 0/y == 0 regardless of y.
    }
    if (z == 0) {
      return *this *= DenseFPS(Mult::invert(other.coeff_));
    } else {
      shift_inplace(-z);
      std::vector<T> y(other.coeff_.begin() + std::min(z, other.size()),
                       other.coeff_.end());
      return *this *= DenseFPS(Mult::invert(std::move(y)));
    }
  }
  friend DenseFPS operator/(const DenseFPS &f, const DenseFPS &g) {
    return DenseFPS(f) /= g;
  }

  // Multiplies by (1 + c * x^k).
  void multiply2_inplace(int k, int c) {
    assert(k > 0);
    if (size() <= dmax()) {
      coeff_.resize(min(size() + k, dmax() + 1), 0);
    }
    for (int i = size() - 1; i >= k; --i) {
      coeff_[i] += coeff_[i - k] * c;
    }
  }
  // Multiplies by (1 + c * x^k).
  DenseFPS multiply2(int k, int c) const {
    DenseFPS res = *this;
    res.multiply2_inplace(k, c);
    return res;
  }

  // Divides by (1 + c * x^k).
  void divide2_inplace(int k, int c) {
    assert(k > 0);
    for (int i = k; i < size(); ++i) {
      coeff_[i] -= coeff_[i - k] * c;
    }
  }
  // Divides by (1 + c * x^k).
  DenseFPS divide2(int k, int c) const {
    DenseFPS res = *this;
    res.divide2_inplace(k, c);
    return res;
  }
};

template<typename FPS>
FPS pow(FPS base, long long t) {
  assert(t >= 0);
  FPS res = {1};
  while (t) {
    if (t & 1) res *= base;
    base *= base;
    t >>= 1;
  }
  return res;
}

constexpr int D = 100005;
using DF = DenseFPS<ArbitraryModMult<Mint, D>>;
using namespace std;

auto solve() {
  int K = in, n = in;
  vector<Mint> C(D, 0);
  REP(i, n) {
    int x = in;
    C[x] = 1;
  }
  DF f(C);

  unordered_map<Int, DF> memo;

  auto powf = [&](auto &powf, Int t) -> DF {
    if (t == 0) return DF{1};
    if (t == 1) return f;
    if (auto it = memo.find(t); it != memo.end()) {
      return it->second;
    }
    DF res;
    if (t & 1) {
      res = powf(powf, t - 1) * f;
    } else {
      res = powf(powf, t / 2);
      res *= res;
    }
    memo[t] = res;
    return res;
  };

  auto dbl = [&](auto &dbl, Int t) -> DF {
    if (t == 0) return DF{0};
    if (t == 1) return f;
    if (t & 1) {
      return dbl(dbl, t - 1) + powf(powf, t);
    } else {
      auto g = dbl(dbl, t / 2);
      return g + g * powf(powf, t / 2);
    }
  };

  auto g = dbl(dbl, K);
  return g[K].val();
}

int main() {
  std::ios::sync_with_stdio(false), cin.tie(nullptr);
  cout << std::fixed << std::setprecision(18);
  const int T = 1;//in;
  REP(t, T) {
    auto ans = solve();
    print(ans);
  }
}
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