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

#include <bits/stdc++.h>
#include <random>

using namespace std;

typedef unsigned long long ull;
typedef long long ll;
typedef double ld;
// #define ll __int128
// #define int ll
// #define int ll
// #define char ll
#define double ld
typedef vector<char> vc;
typedef vector<vc> vvc;
typedef vector<vvc> vvvc;
typedef pair<int, int> pii;
typedef pair<pii, pii> piii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<pii> vpi;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<short> vs;
typedef vector<vs> vvs;
typedef vector<vvs> vvvs;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<vvl> vvvl;
typedef vector<ld> vld;
typedef vector<vld> vvld;
typedef vector<vvld> vvvld;
typedef vector<string> vst;
typedef vector<vst> vvst;
typedef pair<ld, ld> pld;

#define inmin(a, b) a = min(a, (b))
#define inmax(a, b) a = max(a, (b))
#define ALL(a) a.begin(), a.end()
#define RALL(a) a.rbegin(), a.rend()
#define sqr(x) ((x) * (x))
#define fori(i, n) for (int i = 0; i < int(n); ++i)
#define SZ(a) ((int)((a).size()))
#define triple(T) tuple<T, T, T>
#define quad(T) tuple<T, T, T, T>
#define watch(x) cerr << (#x) << " = " << (x) << endl;

#ifdef MAX_HOME
#define cerr cout
#else
#define cerr                                                                   \\
  if (false)                                                                   \\
  cerr
#endif

const double PI = 2 * acos(0.0);
// #define rand shittttty_shit
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
mt19937_64 rng_64(chrono::steady_clock::now().time_since_epoch().count());

const string DIGITS = "0123456789";
const string ALPH = "abcdefghijklmnopqrstuvwxyz";

template <class T0, class T1>
inline ostream &operator<<(ostream &out, pair<T0, T1> &a) {
  return out << "{" << a.first << ", " << a.second << "}";
}

template <class T0, class T1>
inline istream &operator>>(istream &in, pair<T0, T1> &a) {
  return in >> a.first >> a.second;
}

template <class T0, class T1, class T2>
inline ostream &operator<<(ostream &out, tuple<T0, T1, T2> &a) {
  return out << "{" << get<0>(a) << ", " << get<1>(a) << ", " << get<2>(a)
             << "}";
}

template <class T0, class T1, class T2, class T3>
inline ostream &operator<<(ostream &out, tuple<T0, T1, T2, T3> &a) {
  return out << "{" << get<0>(a) << ", " << get<1>(a) << ", " << get<2>(a)
             << ", " << get<3>(a) << "}";
}

template <class T> inline ostream &operator<<(ostream &out, vector<T> &a) {
  out << "[";
  fori(i, a.size()) out << a[i]
                        << vector<string>{", ", "]  "}[i + 1 == a.size()];
  return out;
}

void smain();

signed main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
#ifdef MAX_HOME
  freopen("input.txt", "r", stdin);
  clock_t start = clock();
#endif
  cout << setprecision(12) << fixed;
  smain();
#ifdef MAX_HOME
  cout << "\\n\\nTOTAL EXECUTION TIME: "
       << float(clock() - start) / CLOCKS_PER_SEC << endl;
#endif
  return 0;
}

const int M = 998244353;

int pw(int a, int n = M - 2) {
  int ret = 1;
  while (n) {
    if (n & 1)
      ret = (ll)ret * a % M;
    a = (ll)a * a % M;
    n >>= 1;
  }
  return ret;
}

const int N = 3030;

int dp[N][N];

int sum1[N][N];
int sum2[N][N];

int inv[N];

void insum(int &a, int b) { a = (a + b < M ? a + b : a + b - M); }

void smain() {
  int a, b, c, d;
  cin >> a >> b >> c >> d;
  int n = c - a;
  int m = d - b;

  for (int i = 0; i < N; ++i) {
    inv[i] = pw(i);
  }

  for (int i = 0; i < N; ++i) {
    dp[i][0] = pw(b, i);
    sum2[i][0] = (ll)dp[i][0] * pw(pw(i + a - 1, 0)) % M;
  }
  for (int j = 0; j < N; ++j) {
    dp[0][j] = pw(a, j);
    sum1[0][j] = (ll)dp[0][j] * pw(pw(j + b - 1, 0)) % M;
  }

  dp[0][0] = 1;

  for (int i = 1; i <= n; ++i) {
    for (int j = 1; j <= m; ++j) {
      dp[i][j] = (ll)dp[i - 1][j - 1] * (i + a - 1) % M * (j + b - 1) % M;
      int cur = (ll)sum1[i - 1][j] * pw(j + b - 1, i - 1) % M;
      insum(dp[i][j], cur);

      cur = (ll)sum2[i][j - 1] * pw(i + a - 1, j - 1) % M;
      insum(dp[i][j], cur);

      sum1[i][j] = (ll)dp[i][j] * pw(inv[j + b - 1], i) % M;
      sum2[i][j] = (ll)dp[i][j] * pw(inv[i + a - 1], j) % M;

      if (i) {
        insum(sum1[i][j], sum1[i - 1][j]);
      }
      if (j) {
        insum(sum2[i][j], sum2[i][j - 1]);
      }
    }
  }
  cout << dp[n][m];
}

Error: TLE

Fixed submission:

#include <bits/stdc++.h>
#include <random>

using namespace std;

typedef unsigned long long ull;
typedef long long ll;
typedef double ld;
// #define ll __int128
// #define int ll
// #define int ll
// #define char ll
#define double ld
typedef vector<char> vc;
typedef vector<vc> vvc;
typedef vector<vvc> vvvc;
typedef pair<int, int> pii;
typedef pair<pii, pii> piii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<pii> vpi;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<short> vs;
typedef vector<vs> vvs;
typedef vector<vvs> vvvs;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<vvl> vvvl;
typedef vector<ld> vld;
typedef vector<vld> vvld;
typedef vector<vvld> vvvld;
typedef vector<string> vst;
typedef vector<vst> vvst;
typedef pair<ld, ld> pld;

#define inmin(a, b) a = min(a, (b))
#define inmax(a, b) a = max(a, (b))
#define ALL(a) a.begin(), a.end()
#define RALL(a) a.rbegin(), a.rend()
#define sqr(x) ((x) * (x))
#define fori(i, n) for (int i = 0; i < int(n); ++i)
#define SZ(a) ((int)((a).size()))
#define triple(T) tuple<T, T, T>
#define quad(T) tuple<T, T, T, T>
#define watch(x) cerr << (#x) << " = " << (x) << endl;

#ifdef MAX_HOME
#define cerr cout
#else
#define cerr                                                                   \\
  if (false)                                                                   \\
  cerr
#endif

const double PI = 2 * acos(0.0);
// #define rand shittttty_shit
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
mt19937_64 rng_64(chrono::steady_clock::now().time_since_epoch().count());

const string DIGITS = "0123456789";
const string ALPH = "abcdefghijklmnopqrstuvwxyz";

template <class T0, class T1>
inline ostream &operator<<(ostream &out, pair<T0, T1> &a) {
  return out << "{" << a.first << ", " << a.second << "}";
}

template <class T0, class T1>
inline istream &operator>>(istream &in, pair<T0, T1> &a) {
  return in >> a.first >> a.second;
}

template <class T0, class T1, class T2>
inline ostream &operator<<(ostream &out, tuple<T0, T1, T2> &a) {
  return out << "{" << get<0>(a) << ", " << get<1>(a) << ", " << get<2>(a)
             << "}";
}

template <class T0, class T1, class T2, class T3>
inline ostream &operator<<(ostream &out, tuple<T0, T1, T2, T3> &a) {
  return out << "{" << get<0>(a) << ", " << get<1>(a) << ", " << get<2>(a)
             << ", " << get<3>(a) << "}";
}

template <class T> inline ostream &operator<<(ostream &out, vector<T> &a) {
  out << "[";
  fori(i, a.size()) out << a[i]
                        << vector<string>{", ", "]  "}[i + 1 == a.size()];
  return out;
}

void smain();

signed main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
#ifdef MAX_HOME
  freopen("input.txt", "r", stdin);
  clock_t start = clock();
#endif
  cout << setprecision(12) << fixed;
  smain();
#ifdef MAX_HOME
  cout << "\\n\\nTOTAL EXECUTION TIME: "
       << float(clock() - start) / CLOCKS_PER_SEC << endl;
#endif
  return 0;
}

const int M = 998244353;

int pw(int a, int n = M - 2) {
  int ret = 1;
  while (n) {
    if (n & 1)
      ret = (ll)ret * a % M;
    a = (ll)a * a % M;
    n >>= 1;
  }
  return ret;
}

const int N = 3030;

int dp[N][N];

int sum1[N][N];
int sum2[N][N];

void insum(int &a, int b) { a = (a + b) % M; }

void insub(int &a, int b) { a = (a - b + M) % M; }

void smain() {
  int a, b, c, d;
  cin >> a >> b >> c >> d;
  int n = c - a;
  int m = d - b;

  for (int i = 0; i < N; ++i) {
    dp[i][0] = pw(b, i);
    sum2[i][0] = (ll)dp[i][0] * pw(pw(i + a - 1, 0)) % M;
  }
  for (int j = 0; j < N; ++j) {
    dp[0][j] = pw(a, j);
    sum1[0][j] = (ll)dp[0][j] * pw(pw(j + b - 1, 0)) % M;
  }

  dp[0][0] = 1;

  for (int i = 1; i <= n; ++i) {
    for (int j = 1; j <= m; ++j) {
      dp[i][j] = (ll)dp[i - 1][j - 1] * (i + a - 1) % M * (j + b - 1) % M;
      int cur = (ll)sum1[i - 1][j] * pw(j + b - 1, i - 1) % M;
      insum(dp[i][j], cur);

      cur = (ll)sum2[i][j - 1] * pw(i + a - 1, j - 1) % M;
      insum(dp[i][j], cur);

      sum1[i][j] = (ll)dp[i][j] * pw(pw(j + b - 1, i)) % M;
      sum2[i][j] = (ll)dp[i][j] * pw(pw(i + a - 1, j)) % M;

      if (i) {
        insum(sum1[i][j], sum1[i - 1][j]);
      }
      if (j) {
        insum(sum2[i][j], sum2[i][j - 1]);
      }
    }
  }
  fori(i, n + 1) {
    fori(j, m + 1) {
      cerr << "dp[" << i << "][" << j << "] = " << dp[i][j] << endl;
    }
    //        cerr << '\\n';
  }
  cout << dp[n][m];
}