Problem p02549 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>

#ifdef LOCAL
#include <debug.hpp>
#else
#define debug(...) void()
#endif

using namespace std;

template <typename T> T inverse(T a, T m) {
  T u = 0, v = 1;
  while (a != 0) {
    T t = m / a;
    m -= t * a;
    swap(a, m);
    u -= t * v;
    swap(u, v);
  }
  assert(m == 1);
  return u;
}

template <typename T> class Modular {
public:
  using Type = typename decay<decltype(T::value)>::type;

  constexpr Modular() : value() {}
  template <typename U> Modular(const U &x) { value = normalize(x); }

  template <typename U> static Type normalize(const U &x) {
    Type v;
    if (-mod() <= x && x < mod()) {
      v = static_cast<Type>(x);
    } else {
      v = static_cast<Type>(x % mod());
    }
    if (v < 0)
      v += mod();
    return v;
  }

  const Type &operator()() const { return value; }
  template <typename U> explicit operator U() const {
    return static_cast<U>(value);
  }
  constexpr static Type mod() { return T::value; }

  Modular &operator+=(const Modular &other) {
    if ((value += other.value) >= mod())
      value -= mod();
    return *this;
  }
  Modular &operator-=(const Modular &other) {
    if ((value -= other.value) < 0)
      value += mod();
    return *this;
  }
  template <typename U> Modular &operator+=(const U &other) {
    return *this += Modular(other);
  }
  template <typename U> Modular &operator-=(const U &other) {
    return *this -= Modular(other);
  }
  Modular &operator++() { return *this += 1; }
  Modular &operator--() { return *this -= 1; }
  Modular operator++(int) {
    Modular result(*this);
    *this += 1;
    return result;
  }
  Modular operator--(int) {
    Modular result(*this);
    *this -= 1;
    return result;
  }
  Modular operator-() const { return Modular(-value); }

  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int>::value,
                     Modular>::type &
  operator*=(const Modular &rhs) {
#ifdef _WIN32
    uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
    uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x),
             d, m;
    asm("divl %4; \\n\\t" : "=a"(d), "=d"(m) : "d"(xh), "a"(xl), "r"(mod()));
    value = m;
#else
    value = normalize(static_cast<int64_t>(value) *
                      static_cast<int64_t>(rhs.value));
#endif
    return *this;
  }
  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int64_t>::value,
                     Modular>::type &
  operator*=(const Modular &rhs) {
    int64_t q = static_cast<int64_t>(static_cast<long double>(value) *
                                     rhs.value / mod());
    value = normalize(value * rhs.value - q * mod());
    return *this;
  }
  template <typename U = T>
  typename enable_if<!is_integral<typename Modular<U>::Type>::value,
                     Modular>::type &
  operator*=(const Modular &rhs) {
    value = normalize(value * rhs.value);
    return *this;
  }

  Modular &operator/=(const Modular &other) {
    return *this *= Modular(inverse(other.value, mod()));
  }

  template <typename U> friend const Modular<U> &abs(const Modular<U> &v) {
    return v;
  }

  template <typename U>
  friend bool operator==(const Modular<U> &lhs, const Modular<U> &rhs);

  template <typename U>
  friend bool operator<(const Modular<U> &lhs, const Modular<U> &rhs);

  template <typename U>
  friend std::istream &operator>>(std::istream &stream, Modular<U> &number);

private:
  Type value;
};

template <typename T>
bool operator==(const Modular<T> &lhs, const Modular<T> &rhs) {
  return lhs.value == rhs.value;
}
template <typename T, typename U>
bool operator==(const Modular<T> &lhs, U rhs) {
  return lhs == Modular<T>(rhs);
}
template <typename T, typename U>
bool operator==(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) == rhs;
}

template <typename T>
bool operator!=(const Modular<T> &lhs, const Modular<T> &rhs) {
  return !(lhs == rhs);
}
template <typename T, typename U>
bool operator!=(const Modular<T> &lhs, U rhs) {
  return !(lhs == rhs);
}
template <typename T, typename U>
bool operator!=(U lhs, const Modular<T> &rhs) {
  return !(lhs == rhs);
}

template <typename T>
bool operator<(const Modular<T> &lhs, const Modular<T> &rhs) {
  return lhs.value < rhs.value;
}

template <typename T>
Modular<T> operator+(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) += rhs;
}
template <typename T, typename U>
Modular<T> operator+(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) += rhs;
}
template <typename T, typename U>
Modular<T> operator+(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) += rhs;
}

template <typename T>
Modular<T> operator-(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) -= rhs;
}
template <typename T, typename U>
Modular<T> operator-(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) -= rhs;
}
template <typename T, typename U>
Modular<T> operator-(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) -= rhs;
}

template <typename T>
Modular<T> operator*(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) *= rhs;
}
template <typename T, typename U>
Modular<T> operator*(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) *= rhs;
}
template <typename T, typename U>
Modular<T> operator*(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) *= rhs;
}

template <typename T>
Modular<T> operator/(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) /= rhs;
}
template <typename T, typename U>
Modular<T> operator/(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) /= rhs;
}
template <typename T, typename U>
Modular<T> operator/(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) /= rhs;
}

template <typename T, typename U>
Modular<T> power(const Modular<T> &a, const U &b) {
  assert(b >= 0);
  Modular<T> x = a, res = 1;
  U p = b;
  while (p > 0) {
    if (p & 1)
      res *= x;
    x *= x;
    p >>= 1;
  }
  return res;
}

template <typename T> bool IsZero(const Modular<T> &number) {
  return number() == 0;
}

template <typename T> string to_string(const Modular<T> &number) {
  return to_string(number());
}

template <typename T>
std::ostream &operator<<(std::ostream &stream, const Modular<T> &number) {
  return stream << number();
}

template <typename T>
std::istream &operator>>(std::istream &stream, Modular<T> &number) {
  typename common_type<typename Modular<T>::Type, int64_t>::type x;
  stream >> x;
  number.value = Modular<T>::normalize(x);
  return stream;
}

// using ModType = int;

// struct VarMod { static ModType value; };
// ModType VarMod::value;
// ModType& md = VarMod::value;
// using Mint = Modular<VarMod>;

constexpr int md = 998244353;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;

vector<Mint> fact(1, 1);
vector<Mint> inv_fact(1, 1);

Mint C(int n, int k) {
  if (k < 0 || k > n)
    return 0;
  while ((int)fact.size() < n + 1) {
    fact.emplace_back(fact.back() * (int)fact.size());
    inv_fact.emplace_back(1 / fact.back());
  }
  return fact[n] * inv_fact[k] * inv_fact[n - k];
}

// Mint C(int n, int k) {
//   Mint res = 1;
//   for (int i = 1; i <= k; i++) {
//     res = res * Mint(n - i + 1) / Mint(i);
//   }
//   return res;
// }

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, k;
  cin >> n >> k;
  vector<int> l(k), r(k);
  for (int i = 0; i < k; i++) {
    cin >> l[i] >> r[i];
  }
  int mx = 2 * n;
  vector<Mint> dp(mx, 0);
  dp[0] = 1;
  dp[1] = -1;
  for (int i = 0; i < n; i++) {
    if (i > 0)
      dp[i] += dp[i - 1];
    for (int j = 0; j < k; j++) {
      dp[i + l[j]] += dp[i];
      dp[i + r[j] + 1] -= dp[i];
    }
  }
  cout << dp[n - 1] << '\\n';
  return 0;
}

Error: TLE

Fixed submission:

#include <bits/stdc++.h>

#ifdef LOCAL
#include <debug.hpp>
#else
#define debug(...) void()
#endif

using namespace std;

template <typename T> T inverse(T a, T m) {
  T u = 0, v = 1;
  while (a != 0) {
    T t = m / a;
    m -= t * a;
    swap(a, m);
    u -= t * v;
    swap(u, v);
  }
  assert(m == 1);
  return u;
}

template <typename T> class Modular {
public:
  using Type = typename decay<decltype(T::value)>::type;

  constexpr Modular() : value() {}
  template <typename U> Modular(const U &x) { value = normalize(x); }

  template <typename U> static Type normalize(const U &x) {
    Type v;
    if (-mod() <= x && x < mod()) {
      v = static_cast<Type>(x);
    } else {
      v = static_cast<Type>(x % mod());
    }
    if (v < 0)
      v += mod();
    return v;
  }

  const Type &operator()() const { return value; }
  template <typename U> explicit operator U() const {
    return static_cast<U>(value);
  }
  constexpr static Type mod() { return T::value; }

  Modular &operator+=(const Modular &other) {
    if ((value += other.value) >= mod())
      value -= mod();
    return *this;
  }
  Modular &operator-=(const Modular &other) {
    if ((value -= other.value) < 0)
      value += mod();
    return *this;
  }
  template <typename U> Modular &operator+=(const U &other) {
    return *this += Modular(other);
  }
  template <typename U> Modular &operator-=(const U &other) {
    return *this -= Modular(other);
  }
  Modular &operator++() { return *this += 1; }
  Modular &operator--() { return *this -= 1; }
  Modular operator++(int) {
    Modular result(*this);
    *this += 1;
    return result;
  }
  Modular operator--(int) {
    Modular result(*this);
    *this -= 1;
    return result;
  }
  Modular operator-() const { return Modular(-value); }

  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int>::value,
                     Modular>::type &
  operator*=(const Modular &rhs) {
#ifdef _WIN32
    uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
    uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x),
             d, m;
    asm("divl %4; \\n\\t" : "=a"(d), "=d"(m) : "d"(xh), "a"(xl), "r"(mod()));
    value = m;
#else
    value = normalize(static_cast<int64_t>(value) *
                      static_cast<int64_t>(rhs.value));
#endif
    return *this;
  }
  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int64_t>::value,
                     Modular>::type &
  operator*=(const Modular &rhs) {
    int64_t q = static_cast<int64_t>(static_cast<long double>(value) *
                                     rhs.value / mod());
    value = normalize(value * rhs.value - q * mod());
    return *this;
  }
  template <typename U = T>
  typename enable_if<!is_integral<typename Modular<U>::Type>::value,
                     Modular>::type &
  operator*=(const Modular &rhs) {
    value = normalize(value * rhs.value);
    return *this;
  }

  Modular &operator/=(const Modular &other) {
    return *this *= Modular(inverse(other.value, mod()));
  }

  template <typename U> friend const Modular<U> &abs(const Modular<U> &v) {
    return v;
  }

  template <typename U>
  friend bool operator==(const Modular<U> &lhs, const Modular<U> &rhs);

  template <typename U>
  friend bool operator<(const Modular<U> &lhs, const Modular<U> &rhs);

  template <typename U>
  friend std::istream &operator>>(std::istream &stream, Modular<U> &number);

private:
  Type value;
};

template <typename T>
bool operator==(const Modular<T> &lhs, const Modular<T> &rhs) {
  return lhs.value == rhs.value;
}
template <typename T, typename U>
bool operator==(const Modular<T> &lhs, U rhs) {
  return lhs == Modular<T>(rhs);
}
template <typename T, typename U>
bool operator==(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) == rhs;
}

template <typename T>
bool operator!=(const Modular<T> &lhs, const Modular<T> &rhs) {
  return !(lhs == rhs);
}
template <typename T, typename U>
bool operator!=(const Modular<T> &lhs, U rhs) {
  return !(lhs == rhs);
}
template <typename T, typename U>
bool operator!=(U lhs, const Modular<T> &rhs) {
  return !(lhs == rhs);
}

template <typename T>
bool operator<(const Modular<T> &lhs, const Modular<T> &rhs) {
  return lhs.value < rhs.value;
}

template <typename T>
Modular<T> operator+(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) += rhs;
}
template <typename T, typename U>
Modular<T> operator+(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) += rhs;
}
template <typename T, typename U>
Modular<T> operator+(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) += rhs;
}

template <typename T>
Modular<T> operator-(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) -= rhs;
}
template <typename T, typename U>
Modular<T> operator-(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) -= rhs;
}
template <typename T, typename U>
Modular<T> operator-(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) -= rhs;
}

template <typename T>
Modular<T> operator*(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) *= rhs;
}
template <typename T, typename U>
Modular<T> operator*(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) *= rhs;
}
template <typename T, typename U>
Modular<T> operator*(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) *= rhs;
}

template <typename T>
Modular<T> operator/(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) /= rhs;
}
template <typename T, typename U>
Modular<T> operator/(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) /= rhs;
}
template <typename T, typename U>
Modular<T> operator/(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) /= rhs;
}

template <typename T, typename U>
Modular<T> power(const Modular<T> &a, const U &b) {
  assert(b >= 0);
  Modular<T> x = a, res = 1;
  U p = b;
  while (p > 0) {
    if (p & 1)
      res *= x;
    x *= x;
    p >>= 1;
  }
  return res;
}

template <typename T> bool IsZero(const Modular<T> &number) {
  return number() == 0;
}

template <typename T> string to_string(const Modular<T> &number) {
  return to_string(number());
}

template <typename T>
std::ostream &operator<<(std::ostream &stream, const Modular<T> &number) {
  return stream << number();
}

template <typename T>
std::istream &operator>>(std::istream &stream, Modular<T> &number) {
  typename common_type<typename Modular<T>::Type, int64_t>::type x;
  stream >> x;
  number.value = Modular<T>::normalize(x);
  return stream;
}

// using ModType = int;

// struct VarMod { static ModType value; };
// ModType VarMod::value;
// ModType& md = VarMod::value;
// using Mint = Modular<VarMod>;

constexpr int md = 998244353;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;

vector<Mint> fact(1, 1);
vector<Mint> inv_fact(1, 1);

Mint C(int n, int k) {
  if (k < 0 || k > n)
    return 0;
  while ((int)fact.size() < n + 1) {
    fact.emplace_back(fact.back() * (int)fact.size());
    inv_fact.emplace_back(1 / fact.back());
  }
  return fact[n] * inv_fact[k] * inv_fact[n - k];
}

// Mint C(int n, int k) {
//   Mint res = 1;
//   for (int i = 1; i <= k; i++) {
//     res = res * Mint(n - i + 1) / Mint(i);
//   }
//   return res;
// }

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, k;
  cin >> n >> k;
  vector<int> l(k), r(k);
  for (int i = 0; i < k; i++) {
    cin >> l[i] >> r[i];
  }
  int mx = 2 * n;
  vector<Mint> dp(mx, 0);
  dp[0] = 1;
  for (int i = 0; i < n; i++) {
    vector<Mint> dp2(mx, 0);
    for (int j = 0; j < k; j++) {
      dp2[i + l[j]] += dp[i];
      dp2[i + r[j] + 1] -= dp[i];
    }
    for (int i = 1; i < mx; i++) {
      dp2[i] += dp2[i - 1];
    }
    for (int i = 0; i < mx; i++) {
      dp[i] += dp2[i];
    }
  }
  cout << dp[n - 1] << '\\n';
  return 0;
}