Modint
(Mylib/Number/Mint/mint.cpp)

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• Last update: 2021-04-23 23:44:44+09:00
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Operations

Requirements

Notes

Problems

References

Required by

• Number theoretic transform (Mylib/Convolution/ntt_convolution.cpp)

Verified with

• test/aoj/3119/main.test.cpp
• test/aoj/DPL_5_G/main.table.test.cpp
• test/aoj/DPL_5_G/main.test.cpp
• test/aoj/DPL_5_I/main.table.test.cpp
• test/aoj/DPL_5_I/main.test.cpp
• test/aoj/DPL_5_J/main.test.cpp
• test/yosupo-judge/bernoulli_number/main.test.cpp
• test/yosupo-judge/bitwise_and_convolution/main.or.test.cpp
• test/yosupo-judge/bitwise_and_convolution/main.test.cpp
• test/yosupo-judge/bitwise_xor_convolution/main.test.cpp
• test/yosupo-judge/convolution_mod/main.test.cpp
• test/yosupo-judge/convolution_mod_1000000007/main.test.cpp
• test/yosupo-judge/enumerate_triangles/main.test.cpp
• test/yosupo-judge/exp_of_formal_power_series/main.montgomery.test.cpp
• test/yosupo-judge/exp_of_formal_power_series/main.test.cpp
• test/yosupo-judge/find_linear_recurrence/main.test.cpp
• test/yosupo-judge/inv_of_formal_power_series/main.test.cpp
• test/yosupo-judge/kth_term_of_linearly_recurrent_sequence/main.test.cpp
• test/yosupo-judge/log_of_formal_power_series/main.test.cpp
• test/yosupo-judge/matrix_det/main.test.cpp
• test/yosupo-judge/matrix_product/main.test.cpp
• test/yosupo-judge/multipoint_evaluation/main.test.cpp
• test/yosupo-judge/partition_function/main.fps.test.cpp
• test/yosupo-judge/partition_function/main.test.cpp
• test/yosupo-judge/point_set_range_composite/main.test.cpp
• test/yosupo-judge/polynomial_taylor_shift/main.test.cpp
• test/yosupo-judge/pow_of_formal_power_series/main.test.cpp
• test/yosupo-judge/queue_operate_all_composite/main.test.cpp
• test/yosupo-judge/range_affine_range_sum/main.test.cpp
• test/yosupo-judge/sharp_p_subset_sum/main.test.cpp
• test/yosupo-judge/sqrt_of_formal_power_series/main.test.cpp
• test/yosupo-judge/stirling_number_of_the_first_kind/main.test.cpp
• test/yosupo-judge/stirling_number_of_the_second_kind/main.test.cpp
• test/yosupo-judge/subset_convolution/main.test.cpp
• test/yosupo-judge/sum_of_exponential_times_polynomial_limit/main.test.cpp
• test/yosupo-judge/sum_of_totient_function/main.test.cpp
• test/yosupo-judge/system_of_linear_equations/main.test.cpp
• test/yosupo-judge/vertex_set_path_composite/main.test.cpp
• test/yukicoder/117/main.test.cpp
• test/yukicoder/194/main.test.cpp
• test/yukicoder/235/main.test.cpp
• test/yukicoder/510/main.test.cpp
• test/yukicoder/658/main.test.cpp
• test/yukicoder/660/main.test.cpp
• test/yukicoder/665/main.test.cpp
• test/yukicoder/931/main.test.cpp

Code

#pragma once
#include <iostream>
#include <utility>

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 2 "Mylib/Number/Mint/mint.cpp"
#include <iostream>
#include <utility>

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

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