Problem p02965 (C++)

Buggy submission (status: Runtime Error):
// #define NDEBUG
#include <cstddef>
#include <cstdint>
#include <iostream>
#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;

constexpr usize operator"" _z(unsigned long long x) noexcept {
  return static_cast<usize>(x);
}

class rep {
  const usize f, l;

public:
  class itr {
    friend rep;
    usize i;
    constexpr itr(const usize x) noexcept : i(x) {}

  public:
    void operator++() noexcept { ++i; }
    constexpr usize operator*() const noexcept { return i; }
    constexpr bool operator!=(const itr x) const noexcept { return i != x.i; }
  };
  constexpr rep(const usize first, const usize last) noexcept
      : f(first), l(last) {}
  constexpr itr begin() const noexcept { return itr(f); }
  constexpr itr end() const noexcept { return itr(l); }
};
class revrep {
  const usize f, l;

public:
  class itr {
    friend revrep;
    usize i;
    constexpr itr(usize x) noexcept : i(x) {}

  public:
    void operator++() noexcept { --i; }
    constexpr usize operator*() const noexcept { return i; }
    constexpr bool operator!=(const itr x) const noexcept { return i != x.i; }
  };
  constexpr revrep(usize first, usize last) noexcept : f(--first), l(--last) {}
  constexpr itr begin() const noexcept { return itr(l); }
  constexpr itr end() const noexcept { return itr(f); }
};
template <class T> using vec_alias = std::vector<T>;
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) {
  return a < b ? b - a : a - b;
}
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<u64>(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;
  }
};

} // 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 <cmath>
#include <iostream>
#include <iterator>
#include <map>
#include <numeric>
#include <set>
#include <utility>

namespace n91 {

void main_() {
  using mint = modint<998244353>;
  const usize n = scan<usize>();
  const usize m = scan<usize>();
  const fact_binom<mint> binom((n + m) * 4_z + 1_z);
  const auto h = [&binom](const usize n, const usize m) {
    return binom(n + m - 1_z, m);
  };

  mint ans;

  const auto f = [&h, &binom](const usize n, const usize all,
                              const usize odd_max) {
    mint ret;
    for (const auto odd : rep(0_z, odd_max + 1_z)) {
      if (all < odd) {
        break;
      }
      if ((all - odd) % 2_z == 1_z) {
        continue;
      }
      const usize even = (all - odd) / 2_z;
      ret += h(n, even) * binom(n, odd);
    }
    return ret;
  };

  ans += f(n, m * 3_z, m);

  ans -= f(n - 1_z, m - 1_z, m - 1_z) * static_cast<mint>(n);

  if (m >= 2_z)
    ans -= f(n, m - 2_z, m) * static_cast<mint>(n);

  std::cout << ans.value() << std::endl;
}

} // namespace n91

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


Fixed submission:
// #define NDEBUG
#include <cstddef>
#include <cstdint>
#include <iostream>
#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;

constexpr usize operator"" _z(unsigned long long x) noexcept {
  return static_cast<usize>(x);
}

class rep {
  const usize f, l;

public:
  class itr {
    friend rep;
    usize i;
    constexpr itr(const usize x) noexcept : i(x) {}

  public:
    void operator++() noexcept { ++i; }
    constexpr usize operator*() const noexcept { return i; }
    constexpr bool operator!=(const itr x) const noexcept { return i != x.i; }
  };
  constexpr rep(const usize first, const usize last) noexcept
      : f(first), l(last) {}
  constexpr itr begin() const noexcept { return itr(f); }
  constexpr itr end() const noexcept { return itr(l); }
};
class revrep {
  const usize f, l;

public:
  class itr {
    friend revrep;
    usize i;
    constexpr itr(usize x) noexcept : i(x) {}

  public:
    void operator++() noexcept { --i; }
    constexpr usize operator*() const noexcept { return i; }
    constexpr bool operator!=(const itr x) const noexcept { return i != x.i; }
  };
  constexpr revrep(usize first, usize last) noexcept : f(--first), l(--last) {}
  constexpr itr begin() const noexcept { return itr(l); }
  constexpr itr end() const noexcept { return itr(f); }
};
template <class T> using vec_alias = std::vector<T>;
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) {
  return a < b ? b - a : a - b;
}
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<u64>(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;
  }
};

} // 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 <cmath>
#include <iostream>
#include <iterator>
#include <map>
#include <numeric>
#include <set>
#include <utility>

namespace n91 {

void main_() {
  using mint = modint<998244353>;
  const usize n = scan<usize>();
  const usize m = scan<usize>();
  const fact_binom<mint> binom((n + m) * 4_z + 1_z);
  const auto h = [&binom](const usize n, const usize m) {
    return binom(n + m - 1_z, m);
  };

  mint ans;

  const auto f = [&h, &binom](const usize n, const usize all,
                              const usize odd_max) {
    mint ret;
    for (const auto odd : rep(0_z, odd_max + 1_z)) {
      if (all < odd) {
        break;
      }
      if (n < odd) {
        break;
      }
      if ((all - odd) % 2_z == 1_z) {
        continue;
      }
      const usize even = (all - odd) / 2_z;
      ret += h(n, even) * binom(n, odd);
    }
    return ret;
  };

  ans += f(n, m * 3_z, m);

  ans -= f(n - 1_z, m - 1_z, m - 1_z) * static_cast<mint>(n);

  if (m >= 2_z)
    ans -= f(n, m - 2_z, m) * static_cast<mint>(n);

  std::cout << ans.value() << std::endl;
}

} // namespace n91

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