Problem p02878 (C++)

Buggy submission (status: Runtime Error):
#pragma GCC optimize("O3")
#pragma GCC target("sse4")

#include <bits/stdc++.h>

using namespace std;

typedef double db;
typedef long long ll;
typedef long double ld;
typedef string str;

typedef pair<int, int> pi;
typedef pair<ll, ll> pl;
typedef pair<ld, ld> pd;
typedef complex<ld> cd;

typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<ld> vd;
typedef vector<str> vs;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<cd> vcd;

#define FOR(i, a, b) for (int i = (a); i < (b); i++)
#define F0R(i, a) FOR(i, 0, a)
#define ROF(i, a, b) for (int i = (b)-1; i >= (a); i--)
#define R0F(i, a) ROF(i, 0, a)
#define trav(a, x) for (auto &a : x)

#define mp make_pair
#define pb push_back
#define eb emplace_back
#define f first
#define s second
#define lb lower_bound
#define ub upper_bound

#define sz(x) (int)x.size()
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define rsz resize
#define ins insert

const int MOD = 998244353; // = (119<<23)+1
const ll INF = 1e18;
const int MX = 2e5 + 5;
const ld PI = 4 * atan((ld)1);

template <class T> bool ckmin(T &a, const T &b) { return a > b ? a = b, 1 : 0; }
template <class T> bool ckmax(T &a, const T &b) { return a < b ? a = b, 1 : 0; }

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/rope>

using namespace __gnu_pbds;
using namespace __gnu_cxx;

template <class T>
using Tree =
    tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;

#define ook order_of_key
#define fbo find_by_order

namespace input {
template <class T> void re(complex<T> &x);
template <class T1, class T2> void re(pair<T1, T2> &p);
template <class T> void re(vector<T> &a);
template <class T, size_t SZ> void re(array<T, SZ> &a);

template <class T> void re(T &x) { cin >> x; }
void re(double &x) {
  string t;
  re(t);
  x = stod(t);
}
void re(ld &x) {
  string t;
  re(t);
  x = stold(t);
}
template <class T, class... Ts> void re(T &t, Ts &...ts) {
  re(t);
  re(ts...);
}

template <class T> void re(complex<T> &x) {
  T a, b;
  re(a, b);
  x = cd(a, b);
}
template <class T1, class T2> void re(pair<T1, T2> &p) { re(p.f, p.s); }
template <class T> void re(vector<T> &a) { F0R(i, sz(a)) re(a[i]); }
template <class T, size_t SZ> void re(array<T, SZ> &a) { F0R(i, SZ) re(a[i]); }
} // namespace input

using namespace input;

namespace output {
void pr(int x) { cout << x; }
void pr(long x) { cout << x; }
void pr(ll x) { cout << x; }
void pr(unsigned x) { cout << x; }
void pr(unsigned long x) { cout << x; }
void pr(unsigned long long x) { cout << x; }
void pr(float x) { cout << x; }
void pr(double x) { cout << x; }
void pr(ld x) { cout << x; }
void pr(char x) { cout << x; }
void pr(const char *x) { cout << x; }
void pr(const string &x) { cout << x; }
void pr(bool x) { pr(x ? "true" : "false"); }
template <class T> void pr(const complex<T> &x) { cout << x; }

template <class T1, class T2> void pr(const pair<T1, T2> &x);
template <class T> void pr(const T &x);

template <class T, class... Ts> void pr(const T &t, const Ts &...ts) {
  pr(t);
  pr(ts...);
}
template <class T1, class T2> void pr(const pair<T1, T2> &x) {
  pr("{", x.f, ", ", x.s, "}");
}
template <class T> void pr(const T &x) {
  pr("{"); // const iterator needed for vector<bool>
  bool fst = 1;
  for (const auto &a : x)
    pr(!fst ? ", " : "", a), fst = 0;
  pr("}");
}

void ps() { pr("\n"); } // print w/ spaces
template <class T, class... Ts> void ps(const T &t, const Ts &...ts) {
  pr(t);
  if (sizeof...(ts))
    pr(" ");
  ps(ts...);
}

void pc() { pr("]\n"); } // debug w/ commas
template <class T, class... Ts> void pc(const T &t, const Ts &...ts) {
  pr(t);
  if (sizeof...(ts))
    pr(", ");
  pc(ts...);
}
#define dbg(x...) pr("[", #x, "] = ["), pc(x);
} // namespace output

using namespace output;

namespace io {
void setIn(string s) { freopen(s.c_str(), "r", stdin); }
void setOut(string s) { freopen(s.c_str(), "w", stdout); }
void setIO(string s = "") {
  cin.sync_with_stdio(0);
  cin.tie(0); // fast I/O
  cin.exceptions(
      cin.failbit); // ex. throws exception when you try to read letter into int
  if (sz(s)) {
    setIn(s + ".in"), setOut(s + ".out");
  } // for USACO
}
} // namespace io

using namespace io;

template <class T> T invGeneral(T a, T b) {
  a %= b;
  if (a == 0)
    return b == 1 ? 0 : -1;
  T x = invGeneral(b, a);
  return x == -1 ? -1 : ((1 - (ll)b * x) / a + b) % b;
}

template <class T> struct modular {
  T val;
  explicit operator T() const { return val; }
  modular() { val = 0; }
  modular(const ll &v) {
    val = (-MOD <= v && v <= MOD) ? v : v % MOD;
    if (val < 0)
      val += MOD;
  }

  // friend ostream& operator<<(ostream& os, const modular& a) { return os <<
  // a.val; }
  friend void pr(const modular &a) { pr(a.val); }
  friend void re(modular &a) {
    ll x;
    re(x);
    a = modular(x);
  }

  friend bool operator==(const modular &a, const modular &b) {
    return a.val == b.val;
  }
  friend bool operator!=(const modular &a, const modular &b) {
    return !(a == b);
  }
  friend bool operator<(const modular &a, const modular &b) {
    return a.val < b.val;
  }

  modular operator-() const { return modular(-val); }
  modular &operator+=(const modular &m) {
    if ((val += m.val) >= MOD)
      val -= MOD;
    return *this;
  }
  modular &operator-=(const modular &m) {
    if ((val -= m.val) < 0)
      val += MOD;
    return *this;
  }
  modular &operator*=(const modular &m) {
    val = (ll)val * m.val % MOD;
    return *this;
  }
  friend modular pow(modular a, ll p) {
    modular ans = 1;
    for (; p; p /= 2, a *= a)
      if (p & 1)
        ans *= a;
    return ans;
  }
  friend modular inv(const modular &a) {
    auto i = invGeneral(a.val, MOD);
    assert(i != -1);
    return i;
  } // equivalent to return exp(b,MOD-2) if MOD is prime
  modular &operator/=(const modular &m) { return (*this) *= inv(m); }

  friend modular operator+(modular a, const modular &b) { return a += b; }
  friend modular operator-(modular a, const modular &b) { return a -= b; }
  friend modular operator*(modular a, const modular &b) { return a *= b; }

  friend modular operator/(modular a, const modular &b) { return a /= b; }
};

typedef modular<int> mi;
typedef pair<mi, mi> pmi;
typedef vector<mi> vmi;
typedef vector<pmi> vpmi;

int N, A, B;

vi invs, fac, ifac;
void genFac(int SZ) {
  invs.rsz(SZ), fac.rsz(SZ), ifac.rsz(SZ);
  invs[1] = 1;
  FOR(i, 2, SZ) invs[i] = MOD - (ll)MOD / i * invs[MOD % i] % MOD;
  fac[0] = ifac[0] = 1;
  FOR(i, 1, SZ) {
    fac[i] = (ll)fac[i - 1] * i % MOD;
    ifac[i] = (ll)ifac[i - 1] * invs[i] % MOD;
  }
}
ll comb(int a, int b) {
  if (a < b)
    return 0;
  return (ll)fac[a] * ifac[b] % MOD * ifac[a - b] % MOD;
}

mi path(int a, int b) {
  if (min(a, b) < 0)
    return 0;
  return comb(a + b, b);
}

mi lower(int k) {
  if (k == 0)
    return 1;
  if (B - 1 < k)
    return 0;
  return path(B - 1, k) - path(B, k - 1);
}

int main() {
  genFac(2000005);
  setIO();
  re(N, A, B);
  mi ans = 0;
  F0R(k, min(A, N - B) + 1) {
    if (N - B - k == 0) {
      if (k == A)
        ans += lower(k);
    } else {
      // N-B-k-1 over A-k+1 categories
      ans += comb(N - B - k - 1 + A - k, A - k) * lower(k);
    }
  }
  ps(ans);
  // you should actually read the stuff at the bottom
}

/* stuff you should look for
 * int overflow, array bounds
 * special cases (n=1?), set tle
 * do smth instead of nothing and stay organized
 */


Fixed submission:
#pragma GCC optimize("O3")
#pragma GCC target("sse4")

#include <bits/stdc++.h>

using namespace std;

typedef double db;
typedef long long ll;
typedef long double ld;
typedef string str;

typedef pair<int, int> pi;
typedef pair<ll, ll> pl;
typedef pair<ld, ld> pd;
typedef complex<ld> cd;

typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<ld> vd;
typedef vector<str> vs;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<cd> vcd;

#define FOR(i, a, b) for (int i = (a); i < (b); i++)
#define F0R(i, a) FOR(i, 0, a)
#define ROF(i, a, b) for (int i = (b)-1; i >= (a); i--)
#define R0F(i, a) ROF(i, 0, a)
#define trav(a, x) for (auto &a : x)

#define mp make_pair
#define pb push_back
#define eb emplace_back
#define f first
#define s second
#define lb lower_bound
#define ub upper_bound

#define sz(x) (int)x.size()
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define rsz resize
#define ins insert

const int MOD = 998244353; // = (119<<23)+1
const ll INF = 1e18;
const int MX = 2e5 + 5;
const ld PI = 4 * atan((ld)1);

template <class T> bool ckmin(T &a, const T &b) { return a > b ? a = b, 1 : 0; }
template <class T> bool ckmax(T &a, const T &b) { return a < b ? a = b, 1 : 0; }

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/rope>

using namespace __gnu_pbds;
using namespace __gnu_cxx;

template <class T>
using Tree =
    tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;

#define ook order_of_key
#define fbo find_by_order

namespace input {
template <class T> void re(complex<T> &x);
template <class T1, class T2> void re(pair<T1, T2> &p);
template <class T> void re(vector<T> &a);
template <class T, size_t SZ> void re(array<T, SZ> &a);

template <class T> void re(T &x) { cin >> x; }
void re(double &x) {
  string t;
  re(t);
  x = stod(t);
}
void re(ld &x) {
  string t;
  re(t);
  x = stold(t);
}
template <class T, class... Ts> void re(T &t, Ts &...ts) {
  re(t);
  re(ts...);
}

template <class T> void re(complex<T> &x) {
  T a, b;
  re(a, b);
  x = cd(a, b);
}
template <class T1, class T2> void re(pair<T1, T2> &p) { re(p.f, p.s); }
template <class T> void re(vector<T> &a) { F0R(i, sz(a)) re(a[i]); }
template <class T, size_t SZ> void re(array<T, SZ> &a) { F0R(i, SZ) re(a[i]); }
} // namespace input

using namespace input;

namespace output {
void pr(int x) { cout << x; }
void pr(long x) { cout << x; }
void pr(ll x) { cout << x; }
void pr(unsigned x) { cout << x; }
void pr(unsigned long x) { cout << x; }
void pr(unsigned long long x) { cout << x; }
void pr(float x) { cout << x; }
void pr(double x) { cout << x; }
void pr(ld x) { cout << x; }
void pr(char x) { cout << x; }
void pr(const char *x) { cout << x; }
void pr(const string &x) { cout << x; }
void pr(bool x) { pr(x ? "true" : "false"); }
template <class T> void pr(const complex<T> &x) { cout << x; }

template <class T1, class T2> void pr(const pair<T1, T2> &x);
template <class T> void pr(const T &x);

template <class T, class... Ts> void pr(const T &t, const Ts &...ts) {
  pr(t);
  pr(ts...);
}
template <class T1, class T2> void pr(const pair<T1, T2> &x) {
  pr("{", x.f, ", ", x.s, "}");
}
template <class T> void pr(const T &x) {
  pr("{"); // const iterator needed for vector<bool>
  bool fst = 1;
  for (const auto &a : x)
    pr(!fst ? ", " : "", a), fst = 0;
  pr("}");
}

void ps() { pr("\n"); } // print w/ spaces
template <class T, class... Ts> void ps(const T &t, const Ts &...ts) {
  pr(t);
  if (sizeof...(ts))
    pr(" ");
  ps(ts...);
}

void pc() { pr("]\n"); } // debug w/ commas
template <class T, class... Ts> void pc(const T &t, const Ts &...ts) {
  pr(t);
  if (sizeof...(ts))
    pr(", ");
  pc(ts...);
}
#define dbg(x...) pr("[", #x, "] = ["), pc(x);
} // namespace output

using namespace output;

namespace io {
void setIn(string s) { freopen(s.c_str(), "r", stdin); }
void setOut(string s) { freopen(s.c_str(), "w", stdout); }
void setIO(string s = "") {
  cin.sync_with_stdio(0);
  cin.tie(0); // fast I/O
  cin.exceptions(
      cin.failbit); // ex. throws exception when you try to read letter into int
  if (sz(s)) {
    setIn(s + ".in"), setOut(s + ".out");
  } // for USACO
}
} // namespace io

using namespace io;

template <class T> T invGeneral(T a, T b) {
  a %= b;
  if (a == 0)
    return b == 1 ? 0 : -1;
  T x = invGeneral(b, a);
  return x == -1 ? -1 : ((1 - (ll)b * x) / a + b) % b;
}

template <class T> struct modular {
  T val;
  explicit operator T() const { return val; }
  modular() { val = 0; }
  modular(const ll &v) {
    val = (-MOD <= v && v <= MOD) ? v : v % MOD;
    if (val < 0)
      val += MOD;
  }

  // friend ostream& operator<<(ostream& os, const modular& a) { return os <<
  // a.val; }
  friend void pr(const modular &a) { pr(a.val); }
  friend void re(modular &a) {
    ll x;
    re(x);
    a = modular(x);
  }

  friend bool operator==(const modular &a, const modular &b) {
    return a.val == b.val;
  }
  friend bool operator!=(const modular &a, const modular &b) {
    return !(a == b);
  }
  friend bool operator<(const modular &a, const modular &b) {
    return a.val < b.val;
  }

  modular operator-() const { return modular(-val); }
  modular &operator+=(const modular &m) {
    if ((val += m.val) >= MOD)
      val -= MOD;
    return *this;
  }
  modular &operator-=(const modular &m) {
    if ((val -= m.val) < 0)
      val += MOD;
    return *this;
  }
  modular &operator*=(const modular &m) {
    val = (ll)val * m.val % MOD;
    return *this;
  }
  friend modular pow(modular a, ll p) {
    modular ans = 1;
    for (; p; p /= 2, a *= a)
      if (p & 1)
        ans *= a;
    return ans;
  }
  friend modular inv(const modular &a) {
    auto i = invGeneral(a.val, MOD);
    assert(i != -1);
    return i;
  } // equivalent to return exp(b,MOD-2) if MOD is prime
  modular &operator/=(const modular &m) { return (*this) *= inv(m); }

  friend modular operator+(modular a, const modular &b) { return a += b; }
  friend modular operator-(modular a, const modular &b) { return a -= b; }
  friend modular operator*(modular a, const modular &b) { return a *= b; }

  friend modular operator/(modular a, const modular &b) { return a /= b; }
};

typedef modular<int> mi;
typedef pair<mi, mi> pmi;
typedef vector<mi> vmi;
typedef vector<pmi> vpmi;

int N, A, B;

vi invs, fac, ifac;
void genFac(int SZ) {
  invs.rsz(SZ), fac.rsz(SZ), ifac.rsz(SZ);
  invs[1] = 1;
  FOR(i, 2, SZ) invs[i] = MOD - (ll)MOD / i * invs[MOD % i] % MOD;
  fac[0] = ifac[0] = 1;
  FOR(i, 1, SZ) {
    fac[i] = (ll)fac[i - 1] * i % MOD;
    ifac[i] = (ll)ifac[i - 1] * invs[i] % MOD;
  }
}
ll comb(int a, int b) {
  if (a < b)
    return 0;
  return (ll)fac[a] * ifac[b] % MOD * ifac[a - b] % MOD;
}

mi path(int a, int b) {
  if (min(a, b) < 0)
    return 0;
  return comb(a + b, b);
}

mi lower(int k) {
  if (k == 0)
    return 1;
  if (B - 1 < k)
    return 0;
  return path(B - 1, k) - path(B, k - 1);
}

int main() {
  genFac(20000005);
  setIO();
  re(N, A, B);
  mi ans = 0;
  F0R(k, min(A, N - B) + 1) {
    if (N - B - k == 0) {
      if (k == A)
        ans += lower(k);
    } else {
      // N-B-k-1 over A-k+1 categories
      ans += comb(N - B - k - 1 + A - k, A - k) * lower(k);
    }
  }
  ps(ans);
  // you should actually read the stuff at the bottom
}

/* stuff you should look for
 * int overflow, array bounds
 * special cases (n=1?), set tle
 * do smth instead of nothing and stay organized
 */