Problem p02965 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
#define int long long
#define ll long long
using ull = unsigned long long;
using namespace std;
const int INF = 1ll << 50;
const int MOD = 998244353;
#define dump(x)                                                                \
  if (dbg) {                                                                   \
    cerr << #x << " = " << (x) << endl;                                        \
  }
#define overload4(_1, _2, _3, _4, name, ...) name
#define FOR1(n) for (ll i = 0; i < (n); ++i)
#define FOR2(i, n) for (ll i = 0; i < (n); ++i)
#define FOR3(i, a, b) for (ll i = (a); i < (b); ++i)
#define FOR4(i, a, b, c) for (ll i = (a); i < (b); i += (c))
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FORR(i, a, b) for (int i = (a); i <= (b); ++i)
#define bit(n, k) ((n >> k) & 1) /*nのk bit目*/
template <class T> bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return 1;
  } else
    return 0;
}
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  } else
    return 0;
}
void Yes(bool flag = true) {
  if (flag)
    cout << "Yes" << endl;
  else
    cout << "No" << endl;
}
void No(bool flag = true) { Yes(!flag); }
void YES(bool flag = true) {
  if (flag)
    cout << "YES" << endl;
  else
    cout << "NO" << endl;
}
void NO(bool flag = true) { YES(!flag); }
#define pb push_back
#define mp make_pair
#define eb emplace_back
#define lb lower_bound
#define ub upper_bound
#define all(v) (v).begin(), (v).end()
#define SZ(x) ((int)(x).size())
#define vi vector<int>
// #define P pair<int, int>
// #define V vector<int>
// #define S set<int>
#define itn int
bool dbg = false;
template <uint MD> struct ModInt {
  using M = ModInt;
  const static M G;
  uint v;
  ModInt(ll _v = 0) { set_v(_v % MD + MD); }
  M &set_v(uint _v) {
    v = (_v < MD) ? _v : _v - MD;
    return *this;
  }
  explicit operator bool() const { return v != 0; }
  M operator-() const { return M() - *this; }
  M operator+(const M &r) const { return M().set_v(v + r.v); }
  M operator-(const M &r) const { return M().set_v(v + MD - r.v); }
  M operator*(const M &r) const { return M().set_v(ull(v) * r.v % MD); }
  M operator/(const M &r) const { return *this * r.inv(); }
  M &operator+=(const M &r) { return *this = *this + r; }
  M &operator-=(const M &r) { return *this = *this - r; }
  M &operator*=(const M &r) { return *this = *this * r; }
  M &operator/=(const M &r) { return *this = *this / r; }
  bool operator==(const M &r) const { return v == r.v; }
  M pow(ll n) const {
    M x = *this, r = 1;
    while (n) {
      if (n & 1)
        r *= x;
      x *= x;
      n >>= 1;
    }
    return r;
  }
  M inv() const { return pow(MD - 2); }
  friend ostream &operator<<(ostream &os, const M &r) { return os << r.v; }
};
using Mint = ModInt<MOD>;
// Template by yosupo
const int MN = 1'501'000;
Mint fact[MN], iFac[MN];

void first() {
  fact[0] = Mint(1);
  for (int i = 1; i < MN; i++)
    fact[i] = fact[i - 1] * Mint(i);
  iFac[MN - 1] = fact[MN - 1].inv();
  for (int i = MN - 1; i >= 1; i--) {
    iFac[i - 1] = iFac[i] * Mint(i);
  }
  assert(fact[2345] * iFac[2345] == Mint(1));
}
Mint C(int n, int k) {
  if (n < k || k < 0)
    return Mint(0);
  return fact[n] * iFac[k] * iFac[n - k];
}

int N, M;

void solve() {
  first();
  Mint ans = 0;
  for (int m = M % 2; m <= min(M, N); m += 2) {
    Mint tmp = C(N, m);
    int R = (M - m) / 2 + M;
    tmp *= C(N + R - 1, N - 1);

    Mint tmp2 = C(N + R - M - 1, N - 1) * m * C(N, m);
    Mint tmp3 = C(N + R - M - 2, N - 1) * (N - m) * C(N, m);
    // cerr << tmp << " " << tmp2 << " " << tmp3 << endl;
    tmp -= tmp2 + tmp3;
    ans += tmp;
  }
  cout << ans << endl;
}

signed main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  cin >> N >> M;

  solve();
  return 0;
}


Fixed submission:
#include <bits/stdc++.h>
#define int long long
#define ll long long
using ull = unsigned long long;
using namespace std;
const int INF = 1ll << 50;
const int MOD = 998244353;
#define dump(x)                                                                \
  if (dbg) {                                                                   \
    cerr << #x << " = " << (x) << endl;                                        \
  }
#define overload4(_1, _2, _3, _4, name, ...) name
#define FOR1(n) for (ll i = 0; i < (n); ++i)
#define FOR2(i, n) for (ll i = 0; i < (n); ++i)
#define FOR3(i, a, b) for (ll i = (a); i < (b); ++i)
#define FOR4(i, a, b, c) for (ll i = (a); i < (b); i += (c))
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FORR(i, a, b) for (int i = (a); i <= (b); ++i)
#define bit(n, k) ((n >> k) & 1) /*nのk bit目*/
template <class T> bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return 1;
  } else
    return 0;
}
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  } else
    return 0;
}
void Yes(bool flag = true) {
  if (flag)
    cout << "Yes" << endl;
  else
    cout << "No" << endl;
}
void No(bool flag = true) { Yes(!flag); }
void YES(bool flag = true) {
  if (flag)
    cout << "YES" << endl;
  else
    cout << "NO" << endl;
}
void NO(bool flag = true) { YES(!flag); }
#define pb push_back
#define mp make_pair
#define eb emplace_back
#define lb lower_bound
#define ub upper_bound
#define all(v) (v).begin(), (v).end()
#define SZ(x) ((int)(x).size())
#define vi vector<int>
// #define P pair<int, int>
// #define V vector<int>
// #define S set<int>
#define itn int
bool dbg = false;
template <uint MD> struct ModInt {
  using M = ModInt;
  const static M G;
  uint v;
  ModInt(ll _v = 0) { set_v(_v % MD + MD); }
  M &set_v(uint _v) {
    v = (_v < MD) ? _v : _v - MD;
    return *this;
  }
  explicit operator bool() const { return v != 0; }
  M operator-() const { return M() - *this; }
  M operator+(const M &r) const { return M().set_v(v + r.v); }
  M operator-(const M &r) const { return M().set_v(v + MD - r.v); }
  M operator*(const M &r) const { return M().set_v(ull(v) * r.v % MD); }
  M operator/(const M &r) const { return *this * r.inv(); }
  M &operator+=(const M &r) { return *this = *this + r; }
  M &operator-=(const M &r) { return *this = *this - r; }
  M &operator*=(const M &r) { return *this = *this * r; }
  M &operator/=(const M &r) { return *this = *this / r; }
  bool operator==(const M &r) const { return v == r.v; }
  M pow(ll n) const {
    M x = *this, r = 1;
    while (n) {
      if (n & 1)
        r *= x;
      x *= x;
      n >>= 1;
    }
    return r;
  }
  M inv() const { return pow(MD - 2); }
  friend ostream &operator<<(ostream &os, const M &r) { return os << r.v; }
};
using Mint = ModInt<MOD>;
// Template by yosupo
const int MN = 2'501'000;
Mint fact[MN], iFac[MN];

void first() {
  fact[0] = Mint(1);
  for (int i = 1; i < MN; i++)
    fact[i] = fact[i - 1] * Mint(i);
  iFac[MN - 1] = fact[MN - 1].inv();
  for (int i = MN - 1; i >= 1; i--) {
    iFac[i - 1] = iFac[i] * Mint(i);
  }
  assert(fact[2345] * iFac[2345] == Mint(1));
}
Mint C(int n, int k) {
  if (n < k || k < 0)
    return Mint(0);
  return fact[n] * iFac[k] * iFac[n - k];
}

int N, M;

void solve() {
  first();
  Mint ans = 0;
  for (int m = M % 2; m <= min(M, N); m += 2) {
    Mint tmp = C(N, m);
    int R = (M - m) / 2 + M;
    tmp *= C(N + R - 1, N - 1);

    Mint tmp2 = C(N + R - M - 1, N - 1) * m * C(N, m);
    Mint tmp3 = C(N + R - M - 2, N - 1) * (N - m) * C(N, m);
    // cerr << tmp << " " << tmp2 << " " << tmp3 << endl;
    tmp -= tmp2 + tmp3;
    ans += tmp;
  }
  cout << ans << endl;
}

signed main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  cin >> N >> M;

  solve();
  return 0;
}