test/yukicoder/194/main.test.cpp

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Last update: 2021-04-23 23:44:44+09:00
Problem: https://yukicoder.me/problems/no/194
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#define PROBLEM "https://yukicoder.me/problems/no/194"

#include <algorithm>
#include <iostream>
#include <numeric>
#include <vector>
#include "Mylib/IO/input_vector.cpp"
#include "Mylib/LinearAlgebra/inverse_matrix.cpp"
#include "Mylib/LinearAlgebra/square_matrix.cpp"
#include "Mylib/Number/Mint/mint.cpp"

namespace hl = haar_lib;

using mint = hl::modint<1000000007>;

static int N;
using M = hl::square_matrix_dyn<mint, N>;

std::pair<mint, mint> solve1(int64_t N, int64_t K, std::vector<int> A) {
  M m;

  for (int i = 0; i < N; ++i) m[0][i] = 1;
  for (int i = 0; i < N - 1; ++i) m[i + 1][i] = 1;

  std::reverse(A.begin(), A.end());

  mint f = 0;

  {
    auto m2 = m.pow(K - N);
    for (int i = 0; i < N; ++i) f += m2[0][i] * A[i];
  }

  mint s = std::accumulate(A.begin(), A.end(), mint(0));

  {
    auto c    = hl::inverse_matrix(M::unit() - m).value();
    auto temp = (M::unit() - m.pow(K - N + 1)) * c - M::unit();

    s += dot(temp[0], M::vector_type(A));
  }

  return {f, s};
}

std::pair<mint, mint> solve2(int64_t N, int64_t K, std::vector<int> A) {
  std::vector<mint> v(K);

  mint temp = 0;
  for (int i = 0; i < N; ++i) {
    temp += A[i];
    v[i] = A[i];
  }

  for (int i = N; i < K; ++i) {
    v[i] = temp;
    temp += v[i];
    temp -= v[i - N];
  }

  mint f = v.back();
  mint s = std::accumulate(v.begin(), v.end(), mint(0));

  return {f, s};
}

int main() {
  int64_t K;
  std::cin >> N >> K;

  auto A = hl::input_vector<int>(N);

  auto [f, s] = K > 1000000 ? solve1(N, K, A) : solve2(N, K, A);
  std::cout << f << " " << s << "\n";

  return 0;
}

#line 1 "test/yukicoder/194/main.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/194"

#include <algorithm>
#include <iostream>
#include <numeric>
#include <vector>
#line 4 "Mylib/IO/input_vector.cpp"

namespace haar_lib {
  template <typename T>
  std::vector<T> input_vector(int N) {
    std::vector<T> ret(N);
    for (int i = 0; i < N; ++i) std::cin >> ret[i];
    return ret;
  }

  template <typename T>
  std::vector<std::vector<T>> input_vector(int N, int M) {
    std::vector<std::vector<T>> ret(N);
    for (int i = 0; i < N; ++i) ret[i] = input_vector<T>(M);
    return ret;
  }
}  // namespace haar_lib
#line 2 "Mylib/LinearAlgebra/inverse_matrix.cpp"
#include <optional>
#include <utility>

namespace haar_lib {
  template <typename M>
  std::optional<M> inverse_matrix(M m) {
    using T     = typename M::value_type;
    const int N = m.size();
    M ret       = M::unit();

    for (int i = 0; i < N; ++i) {
      int p = i;
      for (int j = i; j < N; ++j) {
        if (m[i][j] != 0) {
          p = j;
          break;
        }
      }

      std::swap(m[i], m[p]);
      std::swap(ret[i], ret[p]);

      {
        T d = m[i][i];

        if (d == 0) return std::nullopt;

        for (int j = 0; j < N; ++j) {
          m[i][j] /= d;
          ret[i][j] /= d;
        }
      }

      for (int j = 0; j < N; ++j) {
        if (i == j) continue;
        T d = m[j][i] / m[i][i];
        for (int k = 0; k < N; ++k) {
          m[j][k] -= m[i][k] * d;
          ret[j][k] -= ret[i][k] * d;
        }
      }
    }

    return ret;
  }
}  // namespace haar_lib
#line 2 "Mylib/LinearAlgebra/square_matrix.cpp"
#include <cstdint>
#line 6 "Mylib/LinearAlgebra/square_matrix.cpp"

namespace haar_lib {
  template <typename T, int &N>
  class vector_dyn {
  public:
    using value_type = T;

  private:
    std::vector<T> data_;

  public:
    vector_dyn() : data_(N) {}
    vector_dyn(T value) : data_(N, value) {}
    vector_dyn(std::initializer_list<T> list) : data_(N) {
      int i = 0;
      for (auto it = list.begin(); it != list.end(); ++it) data_[i++] = *it;
    }
    vector_dyn(const vector_dyn &that) : data_(that.data_) {}

    template <typename U>
    vector_dyn(const std::vector<U> &that) : data_(that.begin(), that.end()) {}

    bool operator==(const vector_dyn &that) { return data_ == that.data_; }
    bool operator!=(const vector_dyn &that) { return !(*this == that); }

    auto &operator=(const vector_dyn &that) {
      data_ = that.data_;
      return *this;
    }

    auto &operator+=(const vector_dyn &that) {
      for (int i = 0; i < N; ++i) data_[i] += that.data_[i];
      return *this;
    }

    auto &operator-=(const vector_dyn &that) {
      for (int i = 0; i < N; ++i) data_[i] -= that.data_[i];
      return *this;
    }

    friend auto dot(const vector_dyn &a, const vector_dyn &b) {
      T ret = 0;
      for (int i = 0; i < N; ++i) ret += a.data_[i] * b.data_[i];
      return ret;
    }

    auto operator+(const vector_dyn &that) const {
      return vector(*this) += that;
    }

    auto operator-(const vector_dyn &that) const {
      return vector(*this) -= that;
    }

    auto &operator[](int i) { return data_[i]; }
    const auto &operator[](int i) const { return data_[i]; }
    auto begin() const { return data_.begin(); }
    auto end() const { return data_.end(); }

    int size() const { return N; }

    friend std::ostream &operator<<(std::ostream &s, const vector_dyn &a) {
      s << "{";
      for (auto it = a.data_.begin(); it != a.data_.end(); ++it) {
        if (it != a.data_.begin()) s << ",";
        s << *it;
      }
      s << "}";
      return s;
    }
  };

  template <typename T, int &N>
  class square_matrix_dyn {
  public:
    using value_type  = T;
    using vector_type = vector_dyn<T, N>;

  private:
    std::vector<vector_type> data_;

  public:
    square_matrix_dyn() : data_(N, vector_type()) {}
    square_matrix_dyn(const T &val) : data_(N, vector_type(val)) {}
    square_matrix_dyn(std::initializer_list<std::initializer_list<T>> list) : data_(N) {
      int i = 0;
      for (auto it = list.begin(); it != list.end(); ++it) {
        data_[i++] = vector_type(*it);
      }
    }
    square_matrix_dyn(const square_matrix_dyn &that) : data_(that.data_) {}
    square_matrix_dyn(const std::vector<std::vector<T>> &that) : data_(N) {
      for (int i = 0; i < N; ++i) data_[i] = that[i];
    }

    bool operator==(const square_matrix_dyn &that) const { return data_ == that.data_; }
    bool operator!=(const square_matrix_dyn &that) const { return !(*this == that); }

    auto &operator=(const square_matrix_dyn &that) {
      data_ = that.data_;
      return *this;
    }

    auto &operator+=(const square_matrix_dyn &that) {
      for (int i = 0; i < N; ++i) data_[i] += that.data_[i];
      return *this;
    }

    auto &operator-=(const square_matrix_dyn &that) {
      for (int i = 0; i < N; ++i) data_[i] -= that.data_[i];
      return *this;
    }

    auto &operator*=(const square_matrix_dyn &that) {
      square_matrix_dyn ret;
      for (int i = 0; i < N; ++i)
        for (int j = 0; j < N; ++j)
          for (int k = 0; k < N; ++k)
            ret[i][j] += data_[i][k] * that.data_[k][j];
      return *this = ret;
    }

    const auto &operator[](int i) const { return data_[i]; }
    auto &operator[](int i) { return data_[i]; }
    int size() const { return N; }

    static auto unit() {
      square_matrix_dyn ret;
      for (int i = 0; i < N; ++i) ret[i][i] = 1;
      return ret;
    }

    auto operator+(const square_matrix_dyn &that) {
      return square_matrix_dyn(*this) += that;
    }
    auto operator-(const square_matrix_dyn &that) {
      return square_matrix_dyn(*this) -= that;
    }
    auto operator*(const square_matrix_dyn &that) {
      return square_matrix_dyn(*this) *= that;
    }

    auto pow(uint64_t p) const {
      auto ret = unit();
      auto a   = *this;

      while (p > 0) {
        if (p & 1) ret *= a;
        a *= a;
        p >>= 1;
      }

      return ret;
    }

    auto operator*(const vector_type &that) {
      vector_type ret;
      for (int i = 0; i < N; ++i) ret[i] = dot(data_[i], that);
      return ret;
    }
  };
}  // namespace haar_lib
#line 4 "Mylib/Number/Mint/mint.cpp"

namespace haar_lib {
  template <int32_t M>
  class modint {
    uint32_t val_;

  public:
    constexpr static auto mod() { return M; }

    constexpr modint() : val_(0) {}
    constexpr modint(int64_t n) {
      if (n >= M)
        val_ = n % M;
      else if (n < 0)
        val_ = n % M + M;
      else
        val_ = n;
    }

    constexpr auto &operator=(const modint &a) {
      val_ = a.val_;
      return *this;
    }
    constexpr auto &operator+=(const modint &a) {
      if (val_ + a.val_ >= M)
        val_ = (uint64_t) val_ + a.val_ - M;
      else
        val_ += a.val_;
      return *this;
    }
    constexpr auto &operator-=(const modint &a) {
      if (val_ < a.val_) val_ += M;
      val_ -= a.val_;
      return *this;
    }
    constexpr auto &operator*=(const modint &a) {
      val_ = (uint64_t) val_ * a.val_ % M;
      return *this;
    }
    constexpr auto &operator/=(const modint &a) {
      val_ = (uint64_t) val_ * a.inv().val_ % M;
      return *this;
    }

    constexpr auto operator+(const modint &a) const { return modint(*this) += a; }
    constexpr auto operator-(const modint &a) const { return modint(*this) -= a; }
    constexpr auto operator*(const modint &a) const { return modint(*this) *= a; }
    constexpr auto operator/(const modint &a) const { return modint(*this) /= a; }

    constexpr bool operator==(const modint &a) const { return val_ == a.val_; }
    constexpr bool operator!=(const modint &a) const { return val_ != a.val_; }

    constexpr auto &operator++() {
      *this += 1;
      return *this;
    }
    constexpr auto &operator--() {
      *this -= 1;
      return *this;
    }

    constexpr auto operator++(int) {
      auto t = *this;
      *this += 1;
      return t;
    }
    constexpr auto operator--(int) {
      auto t = *this;
      *this -= 1;
      return t;
    }

    constexpr static modint pow(int64_t n, int64_t p) {
      if (p < 0) return pow(n, -p).inv();

      int64_t ret = 1, e = n % M;
      for (; p; (e *= e) %= M, p >>= 1)
        if (p & 1) (ret *= e) %= M;
      return ret;
    }

    constexpr static modint inv(int64_t a) {
      int64_t b = M, u = 1, v = 0;

      while (b) {
        int64_t t = a / b;
        a -= t * b;
        std::swap(a, b);
        u -= t * v;
        std::swap(u, v);
      }

      u %= M;
      if (u < 0) u += M;

      return u;
    }

    constexpr static auto frac(int64_t a, int64_t b) { return modint(a) / modint(b); }

    constexpr auto pow(int64_t p) const { return pow(val_, p); }
    constexpr auto inv() const { return inv(val_); }

    friend constexpr auto operator-(const modint &a) { return modint(M - a.val_); }

    friend constexpr auto operator+(int64_t a, const modint &b) { return modint(a) + b; }
    friend constexpr auto operator-(int64_t a, const modint &b) { return modint(a) - b; }
    friend constexpr auto operator*(int64_t a, const modint &b) { return modint(a) * b; }
    friend constexpr auto operator/(int64_t a, const modint &b) { return modint(a) / b; }

    friend std::istream &operator>>(std::istream &s, modint &a) {
      s >> a.val_;
      return s;
    }
    friend std::ostream &operator<<(std::ostream &s, const modint &a) {
      s << a.val_;
      return s;
    }

    template <int N>
    static auto div() {
      static auto value = inv(N);
      return value;
    }

    explicit operator int32_t() const noexcept { return val_; }
    explicit operator int64_t() const noexcept { return val_; }
  };
}  // namespace haar_lib
#line 11 "test/yukicoder/194/main.test.cpp"

namespace hl = haar_lib;

using mint = hl::modint<1000000007>;

static int N;
using M = hl::square_matrix_dyn<mint, N>;

std::pair<mint, mint> solve1(int64_t N, int64_t K, std::vector<int> A) {
  M m;

  for (int i = 0; i < N; ++i) m[0][i] = 1;
  for (int i = 0; i < N - 1; ++i) m[i + 1][i] = 1;

  std::reverse(A.begin(), A.end());

  mint f = 0;

  {
    auto m2 = m.pow(K - N);
    for (int i = 0; i < N; ++i) f += m2[0][i] * A[i];
  }

  mint s = std::accumulate(A.begin(), A.end(), mint(0));

  {
    auto c    = hl::inverse_matrix(M::unit() - m).value();
    auto temp = (M::unit() - m.pow(K - N + 1)) * c - M::unit();

    s += dot(temp[0], M::vector_type(A));
  }

  return {f, s};
}

std::pair<mint, mint> solve2(int64_t N, int64_t K, std::vector<int> A) {
  std::vector<mint> v(K);

  mint temp = 0;
  for (int i = 0; i < N; ++i) {
    temp += A[i];
    v[i] = A[i];
  }

  for (int i = N; i < K; ++i) {
    v[i] = temp;
    temp += v[i];
    temp -= v[i - N];
  }

  mint f = v.back();
  mint s = std::accumulate(v.begin(), v.end(), mint(0));

  return {f, s};
}

int main() {
  int64_t K;
  std::cin >> N >> K;

  auto A = hl::input_vector<int>(N);

  auto [f, s] = K > 1000000 ? solve1(N, K, A) : solve2(N, K, A);
  std::cout << f << " " << s << "\n";

  return 0;
}

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test/yukicoder/194/main.test.cpp

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