Problem p02634 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>
using namespace std;
#pragma region Macros
typedef long long ll;
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define REP(i, n) FOR(i, 0, n)
#define ALL(x) (x).begin(), (x).end()
// const long long MOD=1e9+7;
const long long MOD = 998244353;
const int INF = 1e9;
const long long IINF = 1e18;
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const char dir[4] = {'D', 'R', 'U', 'L'};
#define LOCAL

template <typename T> istream &operator>>(istream &is, vector<T> &v) {
  for (T &x : v)
    is >> x;
  return is;
}
template <typename T> ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < v.size(); ++i) {
    os << v[i] << (i + 1 == v.size() ? "" : " ");
  }
  return os;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  cout << '(' << p.first << ',' << p.second << ')';
  return os;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, const map<T, U> &m) {
  os << '{';
  for (auto itr = m.begin(); itr != m.end(); ++itr) {
    os << '(' << itr->first << ',' << itr->second << ')';
    if (++itr != m.end())
      os << ',';
    --itr;
  }
  os << '}';
  return os;
}
template <typename T> ostream &operator<<(ostream &os, const set<T> &s) {
  os << '{';
  for (auto itr = s.begin(); itr != s.end(); ++itr) {
    os << *itr;
    if (++itr != s.end())
      os << ',';
    --itr;
  }
  os << '}';
  return os;
}

void debug_out() { cerr << '\\n'; }
template <class Head, class... Tail>
void debug_out(Head &&head, Tail &&...tail) {
  cerr << head;
  if (sizeof...(Tail) > 0)
    cerr << ", ";
  debug_out(move(tail)...);
}
#ifdef LOCAL
#define debug(...)                                                             \\
  cerr << " ";                                                                 \\
  cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]"      \\
       << '\\n';                                                                \\
  cerr << " ";                                                                 \\
  debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

template <typename T> T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; }
template <typename T> T lcm(T x, T y) { return x / gcd(x, y) * y; }

template <class T1, class T2> inline bool chmin(T1 &a, T2 b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T1, class T2> inline bool chmax(T1 &a, T2 b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
#pragma endregion

template <uint_fast64_t Modulus> class modint {
  using u64 = uint_fast64_t;

public:
  u64 a;
  constexpr modint(const u64 x = 0) noexcept
      : a(((x % Modulus) + Modulus) % Modulus) {}
  constexpr u64 &value() noexcept { return a; }
  constexpr const u64 &value() const noexcept { return a; }
  constexpr modint &operator+=(const modint &rhs) noexcept {
    a += rhs.a;
    if (a >= Modulus)
      a -= Modulus;
    return *this;
  }
  constexpr modint operator+(const modint &rhs) const noexcept {
    return modint(*this) += rhs;
  }
  constexpr modint &operator++() noexcept { return ++a, *this; }
  constexpr modint operator++(int) noexcept {
    modint t = *this;
    return ++a, t;
  }
  constexpr modint &operator-=(const modint &rhs) noexcept {
    if (a < rhs.a)
      a += Modulus;
    a -= rhs.a;
    return *this;
  }
  constexpr modint operator-(const modint &rhs) const noexcept {
    return modint(*this) -= rhs;
  }
  constexpr modint &operator--() noexcept { return --a, *this; }
  constexpr modint operator--(int) noexcept {
    modint t = *this;
    return --a, t;
  }
  constexpr modint &operator*=(const modint &rhs) noexcept {
    a = a * rhs.a % Modulus;
    return *this;
  }
  constexpr modint operator*(const modint &rhs) const noexcept {
    return modint(*this) *= rhs;
  }
  constexpr modint &operator/=(modint rhs) noexcept {
    u64 exp = Modulus - 2;
    while (exp) {
      if (exp & 1)
        *this *= rhs;
      rhs *= rhs;
      exp >>= 1;
    }
    return *this;
  }
  constexpr modint operator/(const modint &rhs) const noexcept {
    return modint(*this) /= rhs;
  }
  constexpr modint operator-() const noexcept { return modint(Modulus - a); }
  constexpr bool operator==(const modint &rhs) const noexcept {
    return a == rhs.a;
  }
  constexpr bool operator!=(const modint &rhs) const noexcept {
    return a != rhs.a;
  }
  constexpr bool operator!() const noexcept { return !a; }
  friend constexpr modint pow(modint rhs, long long exp) noexcept {
    modint res{1};
    while (exp) {
      if (exp & 1)
        res *= rhs;
      rhs *= rhs;
      exp >>= 1;
    }
    return res;
  }
  template <class T> friend constexpr modint operator+(T x, modint y) noexcept {
    return modint(x) + y;
  }
  template <class T> friend constexpr modint operator-(T x, modint y) noexcept {
    return modint(x) - y;
  }
  template <class T> friend constexpr modint operator*(T x, modint y) noexcept {
    return modint(x) * y;
  }
  template <class T> friend constexpr modint operator/(T x, modint y) noexcept {
    return modint(x) / y;
  }
  friend ostream &operator<<(ostream &s, const modint &rhs) noexcept {
    return s << rhs.a;
  }
  friend istream &operator>>(istream &s, modint &rhs) noexcept {
    u64 a;
    rhs = modint{(s >> a, a)};
    return s;
  }
};

using mint = modint<MOD>;

const int MAX = 5e5 + 10;
vector<mint> fac(MAX), finv(MAX), inv(MAX);
void COMinit() {
  fac[0] = fac[1] = 1;
  finv[0] = finv[1] = 1;
  inv[1] = 1;
  for (int i = 2; i < MAX; ++i) {
    fac[i] = fac[i - 1] * i;
    inv[i] = -inv[MOD % i] * (MOD / i);
    finv[i] = finv[i - 1] * inv[i];
  }
}
mint COM(int n, int k) {
  if (n < k || n < 0 || k < 0)
    return 0;
  return fac[n] * finv[k] * finv[n - k];
}

// Be careful with the value of MAX and conducting COMinit()

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int A, B, C, D;
  cin >> A >> B >> C >> D;
  if (A == C) {
    cout << pow((mint)A, D - B) << '\\n';
    return 0;
  }
  if (B == D) {
    cout << pow((mint)B, C - A) << '\\n';
    return 0;
  }
  vector<vector<mint>> dp(C + 2, vector<mint>(D + 1, 0));
  dp[A][B] = 1;
  for (int i = A; i <= C; ++i) {
    vector<mint> add(D + 2, 0);
    for (int j = B; j <= D; ++j) {
      dp[i + 1][j] += dp[i][j] * (i == C ? 1 : j);
      /*for (int k=j+1;k<=D;++k){
          dp[i+1][k]+=dp[i][j]*pow((mint)i,k-j);
      }*/
      add[j + 1] += dp[i][j] * i;
    }
    for (int j = 0; j <= D; ++j) {
      add[j + 1] += add[j] * i;
      dp[i + 1][j] += add[j];
    }
  }
  cout << dp[C + 1][D] << '\\n';
}

Error: TLE

Fixed submission:

#include <bits/stdc++.h>
using namespace std;
#pragma region Macros
typedef long long ll;
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define REP(i, n) FOR(i, 0, n)
#define ALL(x) (x).begin(), (x).end()
// const long long MOD=1e9+7;
const long long MOD = 998244353;
const int INF = 1e9;
const long long IINF = 1e18;
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const char dir[4] = {'D', 'R', 'U', 'L'};
#define LOCAL

template <typename T> istream &operator>>(istream &is, vector<T> &v) {
  for (T &x : v)
    is >> x;
  return is;
}
template <typename T> ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < v.size(); ++i) {
    os << v[i] << (i + 1 == v.size() ? "" : " ");
  }
  return os;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  cout << '(' << p.first << ',' << p.second << ')';
  return os;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, const map<T, U> &m) {
  os << '{';
  for (auto itr = m.begin(); itr != m.end(); ++itr) {
    os << '(' << itr->first << ',' << itr->second << ')';
    if (++itr != m.end())
      os << ',';
    --itr;
  }
  os << '}';
  return os;
}
template <typename T> ostream &operator<<(ostream &os, const set<T> &s) {
  os << '{';
  for (auto itr = s.begin(); itr != s.end(); ++itr) {
    os << *itr;
    if (++itr != s.end())
      os << ',';
    --itr;
  }
  os << '}';
  return os;
}

void debug_out() { cerr << '\\n'; }
template <class Head, class... Tail>
void debug_out(Head &&head, Tail &&...tail) {
  cerr << head;
  if (sizeof...(Tail) > 0)
    cerr << ", ";
  debug_out(move(tail)...);
}
#ifdef LOCAL
#define debug(...)                                                             \\
  cerr << " ";                                                                 \\
  cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]"      \\
       << '\\n';                                                                \\
  cerr << " ";                                                                 \\
  debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

template <typename T> T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; }
template <typename T> T lcm(T x, T y) { return x / gcd(x, y) * y; }

template <class T1, class T2> inline bool chmin(T1 &a, T2 b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T1, class T2> inline bool chmax(T1 &a, T2 b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
#pragma endregion

template <uint_fast64_t Modulus> class modint {
  using u64 = uint_fast64_t;

public:
  u64 a;
  constexpr modint(const u64 x = 0) noexcept
      : a(((x % Modulus) + Modulus) % Modulus) {}
  constexpr u64 &value() noexcept { return a; }
  constexpr const u64 &value() const noexcept { return a; }
  constexpr modint &operator+=(const modint &rhs) noexcept {
    a += rhs.a;
    if (a >= Modulus)
      a -= Modulus;
    return *this;
  }
  constexpr modint operator+(const modint &rhs) const noexcept {
    return modint(*this) += rhs;
  }
  constexpr modint &operator++() noexcept { return ++a, *this; }
  constexpr modint operator++(int) noexcept {
    modint t = *this;
    return ++a, t;
  }
  constexpr modint &operator-=(const modint &rhs) noexcept {
    if (a < rhs.a)
      a += Modulus;
    a -= rhs.a;
    return *this;
  }
  constexpr modint operator-(const modint &rhs) const noexcept {
    return modint(*this) -= rhs;
  }
  constexpr modint &operator--() noexcept { return --a, *this; }
  constexpr modint operator--(int) noexcept {
    modint t = *this;
    return --a, t;
  }
  constexpr modint &operator*=(const modint &rhs) noexcept {
    a = a * rhs.a % Modulus;
    return *this;
  }
  constexpr modint operator*(const modint &rhs) const noexcept {
    return modint(*this) *= rhs;
  }
  constexpr modint &operator/=(modint rhs) noexcept {
    u64 exp = Modulus - 2;
    while (exp) {
      if (exp & 1)
        *this *= rhs;
      rhs *= rhs;
      exp >>= 1;
    }
    return *this;
  }
  constexpr modint operator/(const modint &rhs) const noexcept {
    return modint(*this) /= rhs;
  }
  constexpr modint operator-() const noexcept { return modint(Modulus - a); }
  constexpr bool operator==(const modint &rhs) const noexcept {
    return a == rhs.a;
  }
  constexpr bool operator!=(const modint &rhs) const noexcept {
    return a != rhs.a;
  }
  constexpr bool operator!() const noexcept { return !a; }
  friend constexpr modint pow(modint rhs, long long exp) noexcept {
    modint res{1};
    while (exp) {
      if (exp & 1)
        res *= rhs;
      rhs *= rhs;
      exp >>= 1;
    }
    return res;
  }
  template <class T> friend constexpr modint operator+(T x, modint y) noexcept {
    return modint(x) + y;
  }
  template <class T> friend constexpr modint operator-(T x, modint y) noexcept {
    return modint(x) - y;
  }
  template <class T> friend constexpr modint operator*(T x, modint y) noexcept {
    return modint(x) * y;
  }
  template <class T> friend constexpr modint operator/(T x, modint y) noexcept {
    return modint(x) / y;
  }
  friend ostream &operator<<(ostream &s, const modint &rhs) noexcept {
    return s << rhs.a;
  }
  friend istream &operator>>(istream &s, modint &rhs) noexcept {
    u64 a;
    rhs = modint{(s >> a, a)};
    return s;
  }
};

using mint = modint<MOD>;

const int MAX = 5e5 + 10;
vector<mint> fac(MAX), finv(MAX), inv(MAX);
void COMinit() {
  fac[0] = fac[1] = 1;
  finv[0] = finv[1] = 1;
  inv[1] = 1;
  for (int i = 2; i < MAX; ++i) {
    fac[i] = fac[i - 1] * i;
    inv[i] = -inv[MOD % i] * (MOD / i);
    finv[i] = finv[i - 1] * inv[i];
  }
}
mint COM(int n, int k) {
  if (n < k || n < 0 || k < 0)
    return 0;
  return fac[n] * finv[k] * finv[n - k];
}

// Be careful with the value of MAX and conducting COMinit()

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int A, B, C, D;
  cin >> A >> B >> C >> D;
  if (A == C) {
    cout << pow((mint)A, D - B) << '\\n';
    return 0;
  }
  if (B == D) {
    cout << pow((mint)B, C - A) << '\\n';
    return 0;
  }
  vector<vector<mint>> dp(C + 2, vector<mint>(D + 1, 0));
  dp[A][B] = 1;
  for (int i = A; i <= C; ++i) {
    for (int j = B; j <= D; ++j) {
      dp[i + 1][j] += dp[i][j] * (i == C ? 1 : j);
      for (int k = j + 1; k <= D; ++k) {
        dp[i + 1][k] += dp[i][j] * pow((mint)i, k - j);
        ;
      }
    }
  }
  cout << dp[C + 1][D] << '\\n';
}