Problem p03332 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <bits/stdc++.h>
using namespace std;
// #define int long long
// TEMPLATE
// START---------------8<---------------8<---------------8<---------------8<---------------//
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<string> vst;
typedef vector<bool> vb;
typedef vector<ld> vld;
typedef vector<pii> vpii;
typedef vector<pll> vpll;
typedef vector<vector<int>> vvi;
const int INF = (0x7FFFFFFFL);
const ll INFF = (0x7FFFFFFFFFFFFFFFL);
const string ALPHABET = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const int MOD = 998244353;
const string alphabet = "abcdefghijklmnopqrstuvwxyz";
const double PI = acos(-1.0);
const double EPS = 1e-9;
const string Alphabet = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz";
int dx[9] = {1, 0, -1, 0, 1, -1, -1, 1, 0};
int dy[9] = {0, 1, 0, -1, -1, -1, 1, 1, 0};
#define ln '\n'
#define scnaf scanf
#define sacnf scanf
#define sancf scanf
#define SS(type, ...)                                                          \
  type __VA_ARGS__;                                                            \
  MACRO_VAR_Scan(__VA_ARGS__);
template <typename T> void MACRO_VAR_Scan(T &t) { cin >> t; }
template <typename First, typename... Rest>
void MACRO_VAR_Scan(First &first, Rest &...rest) {
  cin >> first;
  MACRO_VAR_Scan(rest...);
}
#define SV(type, c, n)                                                         \
  vector<type> c(n);                                                           \
  for (auto &i : c)                                                            \
    cin >> i;
#define SVV(type, c, n, m)                                                     \
  vector<vector<type>> c(n, vector<type>(m));                                  \
  for (auto &r : c)                                                            \
    for (auto &i : r)                                                          \
      cin >> i;
template <class T, class U>
ostream &operator<<(ostream &o, const pair<T, U> &j) {
  o << "{" << j.first << ", " << j.second << "}";
  return o;
}
template <class T, class U>
ostream &operator<<(ostream &o, const map<T, U> &j) {
  o << "{";
  for (auto t = j.begin(); t != j.end(); ++t)
    o << (t != j.begin() ? ", " : "") << *t;
  o << "}";
  return o;
}
template <class T> ostream &operator<<(ostream &o, const set<T> &j) {
  o << "{";
  for (auto t = j.begin(); t != j.end(); ++t)
    o << (t != j.begin() ? ", " : "") << *t;
  o << "}";
  return o;
}
template <class T> ostream &operator<<(ostream &o, const vector<T> &j) {
  o << "{";
  for (int i = 0; i < (int)j.size(); ++i)
    o << (i > 0 ? ", " : "") << j[i];
  o << "}";
  return o;
}
inline int print(void) {
  cout << endl;
  return 0;
}
template <class Head> int print(Head &&head) {
  cout << head;
  print();
  return 0;
}
template <class Head, class... Tail> int print(Head &&head, Tail &&...tail) {
  cout << head << " ";
  print(forward<Tail>(tail)...);
  return 0;
}
inline int debug(void) {
  cerr << endl;
  return 0;
}
template <class Head> int debug(Head &&head) {
  cerr << head;
  debug();
  return 0;
}
template <class Head, class... Tail> int debug(Head &&head, Tail &&...tail) {
  cerr << head << " ";
  debug(forward<Tail>(tail)...);
  return 0;
}
template <typename T> void PA(T &a) {
  int ASIZE = sizeof(a) / sizeof(a[0]);
  for (int ii = 0; ii < ASIZE; ++ii) {
    cout << a[ii] << " \n"[ii == ASIZE - 1];
  }
}
template <typename T> void PV(T &v) {
  int VSIZE = v.size();
  for (int ii = 0; ii < VSIZE; ++ii) {
    cout << v[ii] << " \n"[ii == VSIZE - 1];
  }
}
#define ER(x) cerr << #x << " = " << (x) << endl;
#define ERV(v)                                                                 \
  {                                                                            \
    cerr << #v << " : ";                                                       \
    for (const auto &xxx : v) {                                                \
      cerr << xxx << " ";                                                      \
    }                                                                          \
    cerr << "\n";                                                              \
  }
inline int YES(bool x) {
  cout << ((x) ? "YES" : "NO") << endl;
  return 0;
}
inline int Yes(bool x) {
  cout << ((x) ? "Yes" : "No") << endl;
  return 0;
}
inline int yes(bool x) {
  cout << ((x) ? "yes" : "no") << endl;
  return 0;
}
inline int yES(bool x) {
  cout << ((x) ? "yES" : "nO") << endl;
  return 0;
}
inline int Yay(bool x) {
  cout << ((x) ? "Yay!" : ":(") << endl;
  return 0;
}
template <typename A, typename B> void sankou(bool x, A a, B b) {
  cout << ((x) ? (a) : (b)) << endl;
}
#define _overload3(_1, _2, _3, name, ...) name
#define _REP(i, n) REPI(i, 0, n)
#define REPI(i, a, b) for (ll i = ll(a); i < ll(b); ++i)
#define REP(...) _overload3(__VA_ARGS__, REPI, _REP, )(__VA_ARGS__)
#define _RREP(i, n) RREPI(i, n, 0)
#define RREPI(i, a, b) for (ll i = ll(a); i >= ll(b); --i)
#define RREP(...) _overload3(__VA_ARGS__, RREPI, _RREP, )(__VA_ARGS__)
#define EACH(e, v) for (auto &e : v)
#define PERM(v)                                                                \
  sort((v).begin(), (v).end());                                                \
  for (bool c##p = 1; c##p; c##p = next_permutation((v).begin(), (v).end()))
#define ADD(a, b) a = (a + ll(b)) % MOD
#define MUL(a, b) a = (a * ll(b)) % MOD
inline ll MOP(ll x, ll n, ll m = MOD) {
  ll r = 1;
  while (n > 0) {
    if (n & 1)
      (r *= x) %= m;
    (x *= x) %= m;
    n >>= 1;
  }
  return r;
}
inline ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
inline ll lcm(ll a, ll b) { return a * b / gcd(a, b); }
inline ll POW(ll a, ll b) {
  ll c = 1ll;
  do {
    if (b & 1)
      c *= 1ll * a;
    a *= 1ll * a;
  } while (b >>= 1);
  return c;
}
template <typename T, typename A, typename B>
inline bool between(T x, A a, B b) {
  return ((a <= x) && (x < b));
}
template <class T> inline T sqr(T x) { return x * x; }
template <typename A, typename B> inline bool chmax(A &a, const B &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <typename A, typename B> inline bool chmin(A &a, const B &b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
#define tmax(x, y, z) max((x), max((y), (z)))
#define tmin(x, y, z) min((x), min((y), (z)))
#define PB push_back
#define MP make_pair
#define MT make_tuple
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
#define SORT(v) sort((v).begin(), (v).end())
#define RSORT(v) sort((v).rbegin(), (v).rend())
#define EXIST(s, e) (find((s).begin(), (s).end(), (e)) != (s).end())
#define EXISTST(s, c) (((s).find(c)) != string::npos)
#define POSL(x, val) (lower_bound(x.begin(), x.end(), val) - x.begin())
#define POSU(x, val) (upper_bound(x.begin(), x.end(), val) - x.begin())
#define GEQ(x, val) (int)(x).size() - POSL((x), (val))
#define GREATER(x, val) (int)(x).size() - POSU((x), (val))
#define LEQ(x, val) POSU((x), (val))
#define LESS(x, val) POSL((x), (val))
#define SZV(a) int((a).size())
#define SZA(a) sizeof(a) / sizeof(a[0])
#define ZERO(a) memset(a, 0, sizeof(a))
#define MINUS(a) memset(a, 0xff, sizeof(a))
#define MEMINF(a) memset(a, 0x3f, sizeof(a))
#define FILL(a, b) memset(a, b, sizeof(a))
#define UNIQUE(v)                                                              \
  sort((v).begin(), (v).end());                                                \
  (v).erase(unique((v).begin(), (v).end()), (v).end())
struct abracadabra {
  abracadabra() {
    cin.tie(0);
    ios::sync_with_stdio(0);
    cout << fixed << setprecision(20);
    cerr << fixed << setprecision(5);
  };
} ABRACADABRA;

// TEMPLATE
// END---------------8<---------------8<---------------8<---------------8<---------------//

/*
・組み合わせ, 順列, 重複組み合わせ
  > 前計算 O(MAX_N + logMOD)
  > クエリ O(1)
[備考] nが負の際, C(n,r) = (-1)^r * C(-n+r-1,r)
[使用例]
COMinit();                   // MAX_Nまでの前計算
cout << nCr(n,r) << endl;    // nCr (0 <= (n,r) <= MAX_N)
cout << nPr(n,r) << endl;    // nPr ( ... )
cout << nHr(n,r) << endl;    // nHr ( ... )
*/

const int MAX_N = 300010;
ll fac[MAX_N], finv[MAX_N], inv[MAX_N];
void COMinit() {
  fac[0] = fac[1] = 1;
  finv[0] = finv[1] = 1;
  inv[1] = 1;
  REP(i, 2, MAX_N) {
    fac[i] = fac[i - 1] * i % MOD;
    inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
    finv[i] = finv[i - 1] * inv[i] % MOD;
  }
}
ll nCr(ll n, ll r) {
  if (r == 0)
    return 1;
  if (r < 0)
    return 0;
  if (n < 0)
    return (r % 2 ? -1 : 1) * nCr(-n + r - 1, r);
  if (n == 0 || n < r)
    return 0;
  return (fac[n] * ((finv[n - r] * finv[r]) % MOD)) % MOD;
}
ll nPr(ll n, ll r) {
  if (r < 0 || n < r)
    return 0;
  else
    return (fac[n] * finv[n - r]) % MOD;
}
ll nHr(ll n, ll r) {
  if (n == 0 && r == 0)
    return 1;
  else
    return nCr(n + r - 1, r);
}

signed main() {

  COMinit();

  SS(ll, N, A, B, K);

  ll res = 0;
  REP(i, N + 1) {
    ll s = K - A * i;
    if (s % B != 0)
      continue;
    ll j = s / B;
    if (j < 0 || j > N)
      continue;
    ll tmp = 0;
    for (int g = max(i + j - N, 0LL); g <= j; ++g) {
      ll p = N - g - (i - g) - (j - g);
      if (i - g < 0 || j - g < 0 || p < 0 || p > N)
        continue;
      // print(i, j, g, i - g, j - g, p);
      ll t = (finv[g] * finv[i - g]) % MOD;
      (t *= finv[j - g]) %= MOD;
      (t *= finv[p]) %= MOD;
      (tmp += t) %= MOD;
    }
    // print(i, j, tmp * fac[N] % MOD);
    (res += (tmp * fac[N]) % MOD) %= MOD;
  }

  print(res);
}


Fixed submission:
#include <bits/stdc++.h>
using namespace std;
// #define int long long
// TEMPLATE
// START---------------8<---------------8<---------------8<---------------8<---------------//
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<string> vst;
typedef vector<bool> vb;
typedef vector<ld> vld;
typedef vector<pii> vpii;
typedef vector<pll> vpll;
typedef vector<vector<int>> vvi;
const int INF = (0x7FFFFFFFL);
const ll INFF = (0x7FFFFFFFFFFFFFFFL);
const string ALPHABET = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const int MOD = 998244353;
const string alphabet = "abcdefghijklmnopqrstuvwxyz";
const double PI = acos(-1.0);
const double EPS = 1e-9;
const string Alphabet = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz";
int dx[9] = {1, 0, -1, 0, 1, -1, -1, 1, 0};
int dy[9] = {0, 1, 0, -1, -1, -1, 1, 1, 0};
#define ln '\n'
#define scnaf scanf
#define sacnf scanf
#define sancf scanf
#define SS(type, ...)                                                          \
  type __VA_ARGS__;                                                            \
  MACRO_VAR_Scan(__VA_ARGS__);
template <typename T> void MACRO_VAR_Scan(T &t) { cin >> t; }
template <typename First, typename... Rest>
void MACRO_VAR_Scan(First &first, Rest &...rest) {
  cin >> first;
  MACRO_VAR_Scan(rest...);
}
#define SV(type, c, n)                                                         \
  vector<type> c(n);                                                           \
  for (auto &i : c)                                                            \
    cin >> i;
#define SVV(type, c, n, m)                                                     \
  vector<vector<type>> c(n, vector<type>(m));                                  \
  for (auto &r : c)                                                            \
    for (auto &i : r)                                                          \
      cin >> i;
template <class T, class U>
ostream &operator<<(ostream &o, const pair<T, U> &j) {
  o << "{" << j.first << ", " << j.second << "}";
  return o;
}
template <class T, class U>
ostream &operator<<(ostream &o, const map<T, U> &j) {
  o << "{";
  for (auto t = j.begin(); t != j.end(); ++t)
    o << (t != j.begin() ? ", " : "") << *t;
  o << "}";
  return o;
}
template <class T> ostream &operator<<(ostream &o, const set<T> &j) {
  o << "{";
  for (auto t = j.begin(); t != j.end(); ++t)
    o << (t != j.begin() ? ", " : "") << *t;
  o << "}";
  return o;
}
template <class T> ostream &operator<<(ostream &o, const vector<T> &j) {
  o << "{";
  for (int i = 0; i < (int)j.size(); ++i)
    o << (i > 0 ? ", " : "") << j[i];
  o << "}";
  return o;
}
inline int print(void) {
  cout << endl;
  return 0;
}
template <class Head> int print(Head &&head) {
  cout << head;
  print();
  return 0;
}
template <class Head, class... Tail> int print(Head &&head, Tail &&...tail) {
  cout << head << " ";
  print(forward<Tail>(tail)...);
  return 0;
}
inline int debug(void) {
  cerr << endl;
  return 0;
}
template <class Head> int debug(Head &&head) {
  cerr << head;
  debug();
  return 0;
}
template <class Head, class... Tail> int debug(Head &&head, Tail &&...tail) {
  cerr << head << " ";
  debug(forward<Tail>(tail)...);
  return 0;
}
template <typename T> void PA(T &a) {
  int ASIZE = sizeof(a) / sizeof(a[0]);
  for (int ii = 0; ii < ASIZE; ++ii) {
    cout << a[ii] << " \n"[ii == ASIZE - 1];
  }
}
template <typename T> void PV(T &v) {
  int VSIZE = v.size();
  for (int ii = 0; ii < VSIZE; ++ii) {
    cout << v[ii] << " \n"[ii == VSIZE - 1];
  }
}
#define ER(x) cerr << #x << " = " << (x) << endl;
#define ERV(v)                                                                 \
  {                                                                            \
    cerr << #v << " : ";                                                       \
    for (const auto &xxx : v) {                                                \
      cerr << xxx << " ";                                                      \
    }                                                                          \
    cerr << "\n";                                                              \
  }
inline int YES(bool x) {
  cout << ((x) ? "YES" : "NO") << endl;
  return 0;
}
inline int Yes(bool x) {
  cout << ((x) ? "Yes" : "No") << endl;
  return 0;
}
inline int yes(bool x) {
  cout << ((x) ? "yes" : "no") << endl;
  return 0;
}
inline int yES(bool x) {
  cout << ((x) ? "yES" : "nO") << endl;
  return 0;
}
inline int Yay(bool x) {
  cout << ((x) ? "Yay!" : ":(") << endl;
  return 0;
}
template <typename A, typename B> void sankou(bool x, A a, B b) {
  cout << ((x) ? (a) : (b)) << endl;
}
#define _overload3(_1, _2, _3, name, ...) name
#define _REP(i, n) REPI(i, 0, n)
#define REPI(i, a, b) for (ll i = ll(a); i < ll(b); ++i)
#define REP(...) _overload3(__VA_ARGS__, REPI, _REP, )(__VA_ARGS__)
#define _RREP(i, n) RREPI(i, n, 0)
#define RREPI(i, a, b) for (ll i = ll(a); i >= ll(b); --i)
#define RREP(...) _overload3(__VA_ARGS__, RREPI, _RREP, )(__VA_ARGS__)
#define EACH(e, v) for (auto &e : v)
#define PERM(v)                                                                \
  sort((v).begin(), (v).end());                                                \
  for (bool c##p = 1; c##p; c##p = next_permutation((v).begin(), (v).end()))
#define ADD(a, b) a = (a + ll(b)) % MOD
#define MUL(a, b) a = (a * ll(b)) % MOD
inline ll MOP(ll x, ll n, ll m = MOD) {
  ll r = 1;
  while (n > 0) {
    if (n & 1)
      (r *= x) %= m;
    (x *= x) %= m;
    n >>= 1;
  }
  return r;
}
inline ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
inline ll lcm(ll a, ll b) { return a * b / gcd(a, b); }
inline ll POW(ll a, ll b) {
  ll c = 1ll;
  do {
    if (b & 1)
      c *= 1ll * a;
    a *= 1ll * a;
  } while (b >>= 1);
  return c;
}
template <typename T, typename A, typename B>
inline bool between(T x, A a, B b) {
  return ((a <= x) && (x < b));
}
template <class T> inline T sqr(T x) { return x * x; }
template <typename A, typename B> inline bool chmax(A &a, const B &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <typename A, typename B> inline bool chmin(A &a, const B &b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
#define tmax(x, y, z) max((x), max((y), (z)))
#define tmin(x, y, z) min((x), min((y), (z)))
#define PB push_back
#define MP make_pair
#define MT make_tuple
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
#define SORT(v) sort((v).begin(), (v).end())
#define RSORT(v) sort((v).rbegin(), (v).rend())
#define EXIST(s, e) (find((s).begin(), (s).end(), (e)) != (s).end())
#define EXISTST(s, c) (((s).find(c)) != string::npos)
#define POSL(x, val) (lower_bound(x.begin(), x.end(), val) - x.begin())
#define POSU(x, val) (upper_bound(x.begin(), x.end(), val) - x.begin())
#define GEQ(x, val) (int)(x).size() - POSL((x), (val))
#define GREATER(x, val) (int)(x).size() - POSU((x), (val))
#define LEQ(x, val) POSU((x), (val))
#define LESS(x, val) POSL((x), (val))
#define SZV(a) int((a).size())
#define SZA(a) sizeof(a) / sizeof(a[0])
#define ZERO(a) memset(a, 0, sizeof(a))
#define MINUS(a) memset(a, 0xff, sizeof(a))
#define MEMINF(a) memset(a, 0x3f, sizeof(a))
#define FILL(a, b) memset(a, b, sizeof(a))
#define UNIQUE(v)                                                              \
  sort((v).begin(), (v).end());                                                \
  (v).erase(unique((v).begin(), (v).end()), (v).end())
struct abracadabra {
  abracadabra() {
    cin.tie(0);
    ios::sync_with_stdio(0);
    cout << fixed << setprecision(20);
    cerr << fixed << setprecision(5);
  };
} ABRACADABRA;

// TEMPLATE
// END---------------8<---------------8<---------------8<---------------8<---------------//

/*
・組み合わせ, 順列, 重複組み合わせ
  > 前計算 O(MAX_N + logMOD)
  > クエリ O(1)
[備考] nが負の際, C(n,r) = (-1)^r * C(-n+r-1,r)
[使用例]
COMinit();                   // MAX_Nまでの前計算
cout << nCr(n,r) << endl;    // nCr (0 <= (n,r) <= MAX_N)
cout << nPr(n,r) << endl;    // nPr ( ... )
cout << nHr(n,r) << endl;    // nHr ( ... )
*/

const int MAX_N = 300010;
ll fac[MAX_N], finv[MAX_N], inv[MAX_N];
void COMinit() {
  fac[0] = fac[1] = 1;
  finv[0] = finv[1] = 1;
  inv[1] = 1;
  REP(i, 2, MAX_N) {
    fac[i] = fac[i - 1] * i % MOD;
    inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
    finv[i] = finv[i - 1] * inv[i] % MOD;
  }
}
ll nCr(ll n, ll r) {
  if (r == 0)
    return 1;
  if (r < 0)
    return 0;
  if (n < 0)
    return (r % 2 ? -1 : 1) * nCr(-n + r - 1, r);
  if (n == 0 || n < r)
    return 0;
  return (fac[n] * ((finv[n - r] * finv[r]) % MOD)) % MOD;
}
ll nPr(ll n, ll r) {
  if (r < 0 || n < r)
    return 0;
  else
    return (fac[n] * finv[n - r]) % MOD;
}
ll nHr(ll n, ll r) {
  if (n == 0 && r == 0)
    return 1;
  else
    return nCr(n + r - 1, r);
}

signed main() {

  COMinit();

  SS(ll, N, A, B, K);

  ll res = 0;
  REP(i, N + 1) {
    ll s = K - A * i;
    if (s % B != 0)
      continue;
    ll j = s / B;
    if (j < 0 || j > N)
      continue;
    ADD(res, nCr(N, i) * nCr(N, j));
  }

  print(res);
}