#404165 (C++14) No.940 ワープ ε=ε=ε=ε=ε=│;p>д＜│

• 問題: No.940 ワープ ε=ε=ε=ε=ε=│;p>д＜│
• ユーザー: noshi91
• 提出日時: 2019-12-03 00:48:28
• 言語: C++14 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 52 ms / 5,000 ms
• コード長: 7,028 bytes
• コンパイル時間: 799 ms
• コンパイル使用メモリ: 76,672 KB
• 実行使用メモリ: 40,740 KB
• 最終ジャッジ日時: 2024-11-28 10:06:26
• 合計ジャッジ時間: 2,129 ms
• ジャッジサーバーID （参考情報）: judge4 / judge5

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 5,248 KB
testcase_01	AC	1 ms; 5,248 KB
testcase_02	AC	2 ms; 5,248 KB
testcase_03	AC	2 ms; 5,248 KB
testcase_04	AC	2 ms; 5,248 KB
testcase_05	AC	2 ms; 5,248 KB
testcase_06	AC	2 ms; 5,248 KB
testcase_07	AC	2 ms; 5,248 KB
testcase_08	AC	2 ms; 5,248 KB
testcase_09	AC	2 ms; 5,248 KB
testcase_10	AC	2 ms; 5,248 KB
testcase_11	AC	2 ms; 5,248 KB
testcase_12	AC	2 ms; 5,248 KB
testcase_13	AC	2 ms; 5,248 KB
testcase_14	AC	2 ms; 5,248 KB
testcase_15	AC	6 ms; 5,760 KB
testcase_16	AC	14 ms; 11,424 KB
testcase_17	AC	25 ms; 19,960 KB
testcase_18	AC	30 ms; 25,216 KB
testcase_19	AC	24 ms; 19,976 KB
testcase_20	AC	39 ms; 31,616 KB
testcase_21	AC	17 ms; 14,164 KB
testcase_22	AC	36 ms; 30,188 KB
testcase_23	AC	15 ms; 11,884 KB
testcase_24	AC	40 ms; 31,024 KB
testcase_25	AC	47 ms; 36,608 KB
testcase_26	AC	52 ms; 40,740 KB

ソースコード

//#define NDEBUG
#include <algorithm>
#include <cstddef>
#include <cstdint>
#include <iostream>
#include <utility>
#include <vector>

namespace n91 {

using i8 = std::int_fast8_t;
using i32 = std::int_fast32_t;
using i64 = std::int_fast64_t;
using u8 = std::uint_fast8_t;
using u32 = std::uint_fast32_t;
using u64 = std::uint_fast64_t;
using isize = std::ptrdiff_t;
using usize = std::size_t;

struct rep {
  struct itr {
    usize i;
    constexpr itr(const usize i) noexcept : i(i) {}
    void operator++() noexcept { ++i; }
    constexpr usize operator*() const noexcept { return i; }
    constexpr bool operator!=(const itr x) const noexcept { return i != x.i; }
  };
  const itr f, l;
  constexpr rep(const usize f, const usize l) noexcept
      : f(std::min(f, l)), l(l) {}
  constexpr auto begin() const noexcept { return f; }
  constexpr auto end() const noexcept { return l; }
};
struct revrep {
  struct itr {
    usize i;
    constexpr itr(const usize i) noexcept : i(i) {}
    void operator++() noexcept { --i; }
    constexpr usize operator*() const noexcept { return i; }
    constexpr bool operator!=(const itr x) const noexcept { return i != x.i; }
  };
  const itr f, l;
  constexpr revrep(const usize f, const usize l) noexcept
      : f(l - 1), l(std::min(f, l) - 1) {}
  constexpr auto begin() const noexcept { return f; }
  constexpr auto end() const noexcept { return l; }
};
template <class T> auto md_vec(const usize n, const T &value) {
  return std::vector<T>(n, value);
}
template <class... Args> auto md_vec(const usize n, Args... args) {
  return std::vector<decltype(md_vec(args...))>(n, md_vec(args...));
}
template <class T> constexpr T difference(const T &a, const T &b) noexcept {
  if (a < b) {
    return b - a;
  } else {
    return a - b;
  }
}
template <class T> void chmin(T &a, const T &b) noexcept {
  if (b < a) {
    a = b;
  }
}
template <class T> void chmax(T &a, const T &b) noexcept {
  if (a < b) {
    a = b;
  }
}
template <class F> class fix_point : private F {
public:
  explicit constexpr fix_point(F &&f) : F(std::forward<F>(f)) {}

  template <class... Args>
  constexpr decltype(auto) operator()(Args &&... args) const {
    return F::operator()(*this, std::forward<Args>(args)...);
  }
};
template <class F> constexpr decltype(auto) make_fix(F &&f) {
  return fix_point<F>(std::forward<F>(f));
}
template <class T> T scan() {
  T ret;
  std::cin >> ret;
  return ret;
}

} // namespace n91
#include <cstdint>

namespace n91 {

constexpr std::uint_fast64_t totient(std::uint_fast64_t x) noexcept {
  using u64 = std::uint_fast64_t;
  u64 ret = x;
  for (u64 i = static_cast<u64>(2); i * i <= x; ++i) {
    if (x % i == static_cast<u64>(0)) {
      ret -= ret / i;
      x /= i;
      while (x % i == static_cast<u64>(0)) {
        x /= i;
      }
    }
  }
  if (x != static_cast<u64>(1)) {
    ret -= ret / x;
  }
  return ret;
}

template <std::uint_fast64_t Modulus,
          std::uint_fast64_t InverseExp =
              totient(Modulus) - static_cast<std::uint_fast64_t>(1)>
class modint {
  using u64 = std::uint_fast64_t;

  static_assert(Modulus < static_cast<u64>(1) << static_cast<u64>(32),
                "Modulus must be less than 2**32");

  u64 a;

  constexpr modint &negate() noexcept {
    if (a != static_cast<u64>(0)) {
      a = Modulus - a;
    }
    return *this;
  }

public:
  constexpr modint(const u64 x = static_cast<u64>(0)) noexcept
      : a(x % Modulus) {}
  constexpr u64 &value() noexcept { return a; }
  constexpr const u64 &value() const noexcept { return a; }
  constexpr modint operator+() const noexcept { return modint(*this); }
  constexpr modint operator-() const noexcept { return modint(*this).negate(); }
  constexpr modint operator+(const modint rhs) const noexcept {
    return modint(*this) += rhs;
  }
  constexpr modint operator-(const modint rhs) const noexcept {
    return modint(*this) -= rhs;
  }
  constexpr modint operator*(const modint rhs) const noexcept {
    return modint(*this) *= rhs;
  }
  constexpr modint operator/(const modint rhs) const noexcept {
    return modint(*this) /= rhs;
  }
  constexpr modint &operator+=(const modint rhs) noexcept {
    a += rhs.a;
    if (a >= Modulus) {
      a -= Modulus;
    }
    return *this;
  }
  constexpr modint &operator-=(const modint rhs) noexcept {
    if (a < rhs.a) {
      a += Modulus;
    }
    a -= rhs.a;
    return *this;
  }
  constexpr modint &operator*=(const modint rhs) noexcept {
    a = a * rhs.a % Modulus;
    return *this;
  }
  constexpr modint &operator/=(modint rhs) noexcept {
    u64 exp = InverseExp;
    while (exp) {
      if (exp % static_cast<u64>(2) != static_cast<u64>(0)) {
        *this *= rhs;
      }
      rhs *= rhs;
      exp /= static_cast<u64>(2);
    }
    return *this;
  }
  constexpr bool operator==(const modint rhs) const noexcept {
    return a == rhs.a;
  }
  constexpr bool operator!=(const modint rhs) const noexcept {
    return a != rhs.a;
  }
};

template <class T, std::uint_fast64_t v> class modint_constant {
public:
  static constexpr T value = static_cast<T>(v);

  using value_type = T;
};
template <class T, std::uint_fast64_t v>
constexpr T modint_constant<T, v>::value;

} // namespace n91
#include <vector>

namespace n91 {

template <class T> class fact_binom {
public:
  using value_type = T;
  using container_type = std::vector<value_type>;
  using size_type = typename container_type::size_type;

private:
  container_type factrial, inv_fact;

public:
  fact_binom() : factrial(), inv_fact() {}
  explicit fact_binom(const size_type n) : factrial(n + 1), inv_fact(n + 1) {
    factrial[0] = static_cast<value_type>(1);
    for (size_type i = 0; i != n; ++i) {
      factrial[i + 1] = static_cast<value_type>(i + 1) * factrial[i];
    }
    inv_fact[n] = static_cast<value_type>(1) / factrial[n];
    for (size_type i = n; i != 0; --i) {
      inv_fact[i - 1] = inv_fact[i] * static_cast<value_type>(i);
    }
  }

  value_type operator()(const size_type n, const size_type r) const {
    return factrial[n] * inv_fact[r] * inv_fact[n - r];
  }
};

} // namespace n91

#include <algorithm>
#include <iostream>
#include <utility>

namespace n91 {

void main_() {
  /*
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  //*/
  using mint = modint<1000000007>;

  const usize x = scan<usize>();
  const usize y = scan<usize>();
  const usize z = scan<usize>();
  if (x == 0 && y == 0 && z == 0) {
    std::cout << 1 << std::endl;
    return;
  }
  const fact_binom<mint> binom((x + y + z + 10) * 2);
  const auto h = [&](const usize n, const usize r) {
    return binom(n + r - 1, n);
  };
  mint ans = 0;
  mint coef = 1;
  const usize s = x + y + z + 1;
  for (usize k = s; --k != 0;) {
    ans += coef * h(x, k) * h(y, k) * h(z, k);
    if ((s - k) % 2 == 0) {
      coef = coef + coef + binom(s, s - k);
    } else {
      coef = coef + coef - binom(s, s - k);
    }
  }
  std::cout << ans.value() << std::endl;
}

} // namespace n91

int main() {
  n91::main_();
  return 0;
}