Problem p02634 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <bits/stdc++.h>
using namespace std;

inline int toInt(string s) {
  int v;
  istringstream sin(s);
  sin >> v;
  return v;
}
template <class T> inline string toString(T x) {
  ostringstream sout;
  sout << x;
  return sout.str();
}

typedef long long ll;
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<long long> VL;
typedef vector<vector<long long>> VVL;
typedef vector<string> VS;
typedef pair<int, int> P;
typedef tuple<int, int, int> tpl;

#define ALL(a) (a).begin(), (a).end()
#define SORT(c) sort((c).begin(), (c).end())
#define REVERSE(c) reverse((c).begin(), (c).end())
#define EXIST(m, v) (m).find((v)) != (m).end()
#define LB(a, x) lower_bound((a).begin(), (a).end(), x) - (a).begin()
#define UB(a, x) upper_bound((a).begin(), (a).end(), x) - (a).begin()

#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define REP(i, n) FOR(i, 0, n)
#define RFOR(i, a, b) for (int i = (a)-1; i >= (b); --i)
#define RREP(i, n) RFOR(i, n, 0)

#define en "\n"

constexpr double EPS = 1e-9;
constexpr double PI = 3.1415926535897932;
constexpr int INF = 2147483647;
constexpr long long LINF = 1LL << 60;
constexpr long long MOD = 998244353;

#define dump(x) cerr << #x << " = " << (x) << endl;
#define debug(x)                                                               \
  cerr << #x << " = " << (x) << " (L" << __LINE__ << ")"                       \
       << " " << __FILE__ << endl;

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;
}

void Main() {
  int A, B, C, D;
  cin >> A >> B >> C >> D;
  ll dp[C + 1][D + 1];
  REP(i, C + 1) REP(j, D + 1) dp[i][j] = 0;

  dp[A][B] = 1;
  REP(i, C + 1) REP(j, D + 1) {
    if (i)
      (dp[i][j] += dp[i - 1][j] * j) %= MOD;
    if (j)
      (dp[i][j] += dp[i][j - 1] * i) %= MOD;
    if (i && j) {
      dp[i][j] -= dp[i - 1][j - 1] * (i - 1) * (j - 1);
      while (dp[i][j] < 0)
        dp[i][j] += MOD;
    }
  }

  cout << dp[C][D] << en;
  return;
}

int main(void) {
  cin.tie(0);
  cout.tie(0);
  ios_base::sync_with_stdio(0);
  cout << fixed << setprecision(15);
  int t = 1; // cin>>t;
  REP(_, t) Main();
  return 0;
}

Fixed submission:
#include <bits/stdc++.h>
using namespace std;

inline int toInt(string s) {
  int v;
  istringstream sin(s);
  sin >> v;
  return v;
}
template <class T> inline string toString(T x) {
  ostringstream sout;
  sout << x;
  return sout.str();
}

typedef long long ll;
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<long long> VL;
typedef vector<vector<long long>> VVL;
typedef vector<string> VS;
typedef pair<int, int> P;
typedef tuple<int, int, int> tpl;

#define ALL(a) (a).begin(), (a).end()
#define SORT(c) sort((c).begin(), (c).end())
#define REVERSE(c) reverse((c).begin(), (c).end())
#define EXIST(m, v) (m).find((v)) != (m).end()
#define LB(a, x) lower_bound((a).begin(), (a).end(), x) - (a).begin()
#define UB(a, x) upper_bound((a).begin(), (a).end(), x) - (a).begin()

#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define REP(i, n) FOR(i, 0, n)
#define RFOR(i, a, b) for (int i = (a)-1; i >= (b); --i)
#define RREP(i, n) RFOR(i, n, 0)

#define en "\n"

constexpr double EPS = 1e-9;
constexpr double PI = 3.1415926535897932;
constexpr int INF = 2147483647;
constexpr long long LINF = 1LL << 60;
constexpr long long MOD = 998244353;

#define dump(x) cerr << #x << " = " << (x) << endl;
#define debug(x)                                                               \
  cerr << #x << " = " << (x) << " (L" << __LINE__ << ")"                       \
       << " " << __FILE__ << endl;

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;
}

void Main() {
  int A, B, C, D;
  cin >> A >> B >> C >> D;
  ll dp[C + 1][D + 1];
  REP(i, C + 1) REP(j, D + 1) dp[i][j] = 0;

  dp[A][B] = 1;
  REP(i, C + 1) REP(j, D + 1) {
    if (i)
      (dp[i][j] += dp[i - 1][j] * j) %= MOD;
    if (j)
      (dp[i][j] += dp[i][j - 1] * i) %= MOD;
    if (i && j) {
      dp[i][j] -= (dp[i - 1][j - 1] * (i - 1) * (j - 1)) % MOD;
      if (dp[i][j] < 0)
        dp[i][j] += MOD;
    }
  }

  cout << dp[C][D] << en;
  return;
}

int main(void) {
  cin.tie(0);
  cout.tie(0);
  ios_base::sync_with_stdio(0);
  cout << fixed << setprecision(15);
  int t = 1; // cin>>t;
  REP(_, t) Main();
  return 0;
}