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

#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define rrep(i, a, b) for (int i = (a); i < (b); ++i)
#define PI acos(-1)
#define pcnt __builtin_popcountll
#define rng(a) a.begin(), a.end()
#define rrng(a) a.rbegin(), a.rend()
#define sz(x) (int)(x).size()
#define v(T) vector<T>
#define vv(T) v(v(T))
#define fi first
#define se second

using namespace std;
using ll = long long;
using ld = long double;
using P = pair<int, int>;
using LP = pair<ll, ll>;
using vi = vector<int>;
using vvi = vector<vi>;
using vl = vector<ll>;
using vvl = vector<vl>;
using tl = tuple<ll, ll, ll>;

template <typename T> inline istream &operator>>(istream &i, v(T) & v) {
  rep(j, sz(v)) i >> v[j];
  return i;
}
template <typename T1, typename T2>
inline istream &operator>>(istream &i, pair<T1, T2> &v) {
  return i >> v.fi >> v.se;
}
template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}

const int mod = 998244353;
struct mint {
  ll x; // using long long ll;
  mint(ll x = 0) : x((x % mod + mod) % mod) {}
  mint operator-() const { return mint(-x); }
  mint &operator+=(const mint a) {
    if ((x += a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator-=(const mint a) {
    if ((x += mod - a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator*=(const mint a) {
    (x *= a.x) %= mod;
    return *this;
  }
  mint operator+(const mint a) const { return mint(*this) += a; }
  mint operator-(const mint a) const { return mint(*this) -= a; }
  mint operator*(const mint a) const { return mint(*this) *= a; }
  mint pow(ll t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }

  // for prime mod
  mint inv() const { return pow(mod - 2); }
  mint &operator/=(const mint a) { return *this *= a.inv(); }
  mint operator/(const mint a) const { return mint(*this) /= a; }
};
istream &operator>>(istream &is, const mint &a) { return is >> a.x; }
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }

ll INF = 1001001001;
ll LINF = 1001001001001001001ll;

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);

  ll a, b, c, d;
  cin >> a >> b >> c >> d;

  vector<vector<vector<mint>>> dp(c + 2,
                                  vector<vector<mint>>(d + 2, vector<mint>(2)));
  dp[a][b][1] = 1;
  rrep(i, a, c + 1) rrep(j, b, d + 1) {
    dp[i][j + 1][1] += dp[i][j][0];
    dp[i][j + 1][1] += dp[i][j][1] * i;
    dp[i + 1][j][0] += (dp[i][j][0] + dp[i][j][1]) * j;
  }
  cout << dp[c][d][0] + dp[c][d][1] << endl;
}

Error: TLE

Fixed submission:

#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define rrep(i, a, b) for (int i = (a); i < (b); ++i)
#define PI acos(-1)
#define pcnt __builtin_popcountll
#define rng(a) a.begin(), a.end()
#define rrng(a) a.rbegin(), a.rend()
#define sz(x) (int)(x).size()
#define v(T) vector<T>
#define vv(T) v(v(T))
#define fi first
#define se second

using namespace std;
using ll = long long;
using ld = long double;
using P = pair<int, int>;
using LP = pair<ll, ll>;
using vi = vector<int>;
using vvi = vector<vi>;
using vl = vector<ll>;
using vvl = vector<vl>;
using tl = tuple<ll, ll, ll>;

template <typename T> inline istream &operator>>(istream &i, v(T) & v) {
  rep(j, sz(v)) i >> v[j];
  return i;
}
template <typename T1, typename T2>
inline istream &operator>>(istream &i, pair<T1, T2> &v) {
  return i >> v.fi >> v.se;
}
template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}

const int mod = 998244353;
struct mint {
  ll x; // using long long ll;
  mint(ll x = 0) : x((x % mod + mod) % mod) {}
  mint operator-() const { return mint(-x); }
  mint &operator+=(const mint a) {
    if ((x += a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator-=(const mint a) {
    if ((x += mod - a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator*=(const mint a) {
    (x *= a.x) %= mod;
    return *this;
  }
  mint operator+(const mint a) const { return mint(*this) += a; }
  mint operator-(const mint a) const { return mint(*this) -= a; }
  mint operator*(const mint a) const { return mint(*this) *= a; }
  mint pow(ll t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }

  // for prime mod
  mint inv() const { return pow(mod - 2); }
  mint &operator/=(const mint a) { return *this *= a.inv(); }
  mint operator/(const mint a) const { return mint(*this) /= a; }
};
istream &operator>>(istream &is, const mint &a) { return is >> a.x; }
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }

ll INF = 1001001001;
ll LINF = 1001001001001001001ll;

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);

  ll a, b, c, d;
  cin >> a >> b >> c >> d;

  vector<vector<vector<mint>>> dp(c + 2,
                                  vector<vector<mint>>(d + 2, vector<mint>(3)));
  dp[a][b][0] = 1;
  rrep(i, a, c + 1) rrep(j, b, d + 1) {
    dp[i][j][0] += dp[i - 1][j][0] * j;
    dp[i][j][0] += dp[i][j - 1][0] * i;
    dp[i][j][1] += dp[i - 1][j - 1][0] * (j - 1) + dp[i][j - 1][1] * i;
    dp[i][j][2] += dp[i - 1][j - 1][0] * (i - 1) + dp[i - 1][j][2] * j;
    if (i > a && j > b)
      dp[i][j][0] = (dp[i][j][0] - dp[i][j][1] - dp[i][j][2]) / 2 +
                    dp[i][j][1] + dp[i][j][2];
  }
  cout << dp[c][d][0] << endl;
}