Problem p02965 (C++)

Buggy submission (status: Runtime Error):
#define _CRT_SECURE_NO_WARNINGS
#pragma target("avx")
#pragma optimize("O3")
#pragma optimize("unroll-loops")
#include <algorithm>
#include <bitset>
#include <cassert>
#include <cfloat>
#include <climits>
#include <cmath>
#include <complex>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <memory>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
#define rep(i, n) for (int i = 0; i < (lint)(n); i++)
#define REP(i, n) for (int i = 1; i <= (lint)(n); i++)
#define all(V) V.begin(), V.end()
typedef long long lint;
typedef std::pair<lint, lint> P;
constexpr int INF = INT_MAX / 2;
constexpr lint LINF = LLONG_MAX / 2;
constexpr double eps = 1e-9;
constexpr double PI = 3.141592653589793238462643383279;
template <class T>
class prique : public std::priority_queue<T, std::vector<T>, std::greater<T>> {
};
template <class T, class U> inline bool chmax(T &lhs, const U &rhs) {
  if (lhs < rhs) {
    lhs = rhs;
    return 1;
  }
  return 0;
}
template <class T, class U> inline bool chmin(T &lhs, const U &rhs) {
  if (lhs > rhs) {
    lhs = rhs;
    return 1;
  }
  return 0;
}
inline lint gcd(lint a, lint b) {
  while (b) {
    lint c = a;
    a = b;
    b = c % b;
  }
  return a;
}
inline lint lcm(lint a, lint b) { return a / gcd(a, b) * b; }
bool isprime(lint n) {
  if (n == 1)
    return false;
  for (int i = 2; i * i <= n; i++) {
    if (n % i == 0)
      return false;
  }
  return true;
}
template <typename T> T mypow(T a, unsigned int b) {
  if (!b)
    return T(1);
  if (b & 1)
    return mypow(a, b - 1) * a;
  T memo = mypow(a, b >> 1);
  return memo * memo;
}
lint modpow(lint a, lint b, lint m) {
  if (!b)
    return 1;
  if (b & 1)
    return modpow(a, b - 1, m) * a % m;
  lint memo = modpow(a, b >> 1, m);
  return memo * memo % m;
}
template <typename T> void printArray(std::vector<T> &vec) {
  rep(i, vec.size() - 1) std::cout << vec[i] << " ";
  std::cout << vec.back() << std::endl;
}
template <typename T> void printArray(T l, T r) {
  T rprev = r;
  rprev--;
  for (T i = l; i != rprev; i++) {
    std::cout << *i << " ";
  }
  std::cout << *rprev << std::endl;
}
template <unsigned int modulo = 998244353> class ModInt {
  lint value;

public:
  ModInt() : value(0) {}
  template <typename T> ModInt(T value = 0) : value(value) {
    if (value < 0)
      value = -(lint)(-value % modulo) + modulo;
    this->value = value % modulo;
  }
  inline operator int() const { return value; }
  inline ModInt &operator+=(const ModInt &x) {
    value += x.value;
    if (value >= modulo)
      value -= modulo;
    return *this;
  }
  inline ModInt &operator++() {
    if (value == modulo - 1)
      value = 0;
    else
      value++;
    return *this;
  }
  inline ModInt operator-() const { return ModInt(0) -= *this; }
  inline ModInt &operator-=(const ModInt &x) {
    value -= x.value;
    if (value < 0)
      value += modulo;
    return *this;
  }
  inline ModInt &operator--() {
    if (value == 0)
      value = modulo - 1;
    else
      value--;
    return *this;
  }
  inline ModInt &operator*=(const ModInt &x) {
    value = value * x.value % modulo;
    return *this;
  }
  inline ModInt &operator/=(ModInt rhs) {
    int exp = modulo - 2;
    while (exp) {
      if (exp & 1)
        *this *= rhs;
      rhs *= rhs;
      exp >>= 1;
    }
    return *this;
  }
  template <typename T> ModInt operator+(const T &rhs) const {
    return ModInt(*this) += rhs;
  }
  template <typename T> ModInt &operator+=(const T &rhs) {
    return operator+=(ModInt(rhs));
  }
  template <typename T> ModInt operator-(const T &rhs) const {
    return ModInt(*this) -= rhs;
  }
  template <typename T> ModInt &operator-=(const T &rhs) {
    return operator-=(ModInt(rhs));
  }
  template <typename T> ModInt operator*(const T &rhs) const {
    return ModInt(*this) *= rhs;
  }
  template <typename T> ModInt &operator*=(const T &rhs) {
    return operator*=(ModInt(rhs));
  }
  template <typename T> ModInt operator/(const T &rhs) const {
    return ModInt(*this) /= rhs;
  }
  template <typename T> ModInt &operator/=(const T &rhs) {
    return operator/=(ModInt(rhs));
  }
};
template <unsigned int T>
std::istream &operator>>(std::istream &ist, ModInt<T> &x) {
  lint a;
  ist >> a;
  x = a;
  return ist;
}
int n, m;
ModInt<> fact[2000010], inv[2000010];
ModInt<> comb(int a, int b) { return fact[a] * inv[a - b] * inv[b]; }
ModInt<> comb2(int a, int b) { return comb(a + b - 1, b - 1); }
int main() {
  std::cin >> n >> m;
  fact[0] = 1;
  REP(i, 2000000) fact[i] = fact[i - 1] * i;
  inv[2000000] = ModInt<>(1) / fact[2000000];
  for (int i = 1999999; i >= 0; i--)
    inv[i] = inv[i + 1] * (i + 1);
  ModInt<> ans = 0;
  for (int i = m; i >= 0; i -= 2) {
    ans += comb(n, i) * comb2((3 * m - i) / 2, n) -
           (comb(n, i) * comb2((m - i) / 2, n) -
            comb(n - 1, i) * comb2((m - i) / 2, n - 1)) *
               n;
  }
  std::cout << ans << std::endl;
  return 0;
}


Fixed submission:
#define _CRT_SECURE_NO_WARNINGS
#pragma target("avx")
#pragma optimize("O3")
#pragma optimize("unroll-loops")
#include <algorithm>
#include <bitset>
#include <cassert>
#include <cfloat>
#include <climits>
#include <cmath>
#include <complex>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <memory>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
#define rep(i, n) for (int i = 0; i < (lint)(n); i++)
#define REP(i, n) for (int i = 1; i <= (lint)(n); i++)
#define all(V) V.begin(), V.end()
typedef long long lint;
typedef std::pair<lint, lint> P;
constexpr int INF = INT_MAX / 2;
constexpr lint LINF = LLONG_MAX / 2;
constexpr double eps = 1e-9;
constexpr double PI = 3.141592653589793238462643383279;
template <class T>
class prique : public std::priority_queue<T, std::vector<T>, std::greater<T>> {
};
template <class T, class U> inline bool chmax(T &lhs, const U &rhs) {
  if (lhs < rhs) {
    lhs = rhs;
    return 1;
  }
  return 0;
}
template <class T, class U> inline bool chmin(T &lhs, const U &rhs) {
  if (lhs > rhs) {
    lhs = rhs;
    return 1;
  }
  return 0;
}
inline lint gcd(lint a, lint b) {
  while (b) {
    lint c = a;
    a = b;
    b = c % b;
  }
  return a;
}
inline lint lcm(lint a, lint b) { return a / gcd(a, b) * b; }
bool isprime(lint n) {
  if (n == 1)
    return false;
  for (int i = 2; i * i <= n; i++) {
    if (n % i == 0)
      return false;
  }
  return true;
}
template <typename T> T mypow(T a, unsigned int b) {
  if (!b)
    return T(1);
  if (b & 1)
    return mypow(a, b - 1) * a;
  T memo = mypow(a, b >> 1);
  return memo * memo;
}
lint modpow(lint a, lint b, lint m) {
  if (!b)
    return 1;
  if (b & 1)
    return modpow(a, b - 1, m) * a % m;
  lint memo = modpow(a, b >> 1, m);
  return memo * memo % m;
}
template <typename T> void printArray(std::vector<T> &vec) {
  rep(i, vec.size() - 1) std::cout << vec[i] << " ";
  std::cout << vec.back() << std::endl;
}
template <typename T> void printArray(T l, T r) {
  T rprev = r;
  rprev--;
  for (T i = l; i != rprev; i++) {
    std::cout << *i << " ";
  }
  std::cout << *rprev << std::endl;
}
template <unsigned int modulo = 998244353> class ModInt {
  lint value;

public:
  ModInt() : value(0) {}
  template <typename T> ModInt(T value = 0) : value(value) {
    if (value < 0)
      value = -(lint)(-value % modulo) + modulo;
    this->value = value % modulo;
  }
  inline operator int() const { return value; }
  inline ModInt &operator+=(const ModInt &x) {
    value += x.value;
    if (value >= modulo)
      value -= modulo;
    return *this;
  }
  inline ModInt &operator++() {
    if (value == modulo - 1)
      value = 0;
    else
      value++;
    return *this;
  }
  inline ModInt operator-() const { return ModInt(0) -= *this; }
  inline ModInt &operator-=(const ModInt &x) {
    value -= x.value;
    if (value < 0)
      value += modulo;
    return *this;
  }
  inline ModInt &operator--() {
    if (value == 0)
      value = modulo - 1;
    else
      value--;
    return *this;
  }
  inline ModInt &operator*=(const ModInt &x) {
    value = value * x.value % modulo;
    return *this;
  }
  inline ModInt &operator/=(ModInt rhs) {
    int exp = modulo - 2;
    while (exp) {
      if (exp & 1)
        *this *= rhs;
      rhs *= rhs;
      exp >>= 1;
    }
    return *this;
  }
  template <typename T> ModInt operator+(const T &rhs) const {
    return ModInt(*this) += rhs;
  }
  template <typename T> ModInt &operator+=(const T &rhs) {
    return operator+=(ModInt(rhs));
  }
  template <typename T> ModInt operator-(const T &rhs) const {
    return ModInt(*this) -= rhs;
  }
  template <typename T> ModInt &operator-=(const T &rhs) {
    return operator-=(ModInt(rhs));
  }
  template <typename T> ModInt operator*(const T &rhs) const {
    return ModInt(*this) *= rhs;
  }
  template <typename T> ModInt &operator*=(const T &rhs) {
    return operator*=(ModInt(rhs));
  }
  template <typename T> ModInt operator/(const T &rhs) const {
    return ModInt(*this) /= rhs;
  }
  template <typename T> ModInt &operator/=(const T &rhs) {
    return operator/=(ModInt(rhs));
  }
};
template <unsigned int T>
std::istream &operator>>(std::istream &ist, ModInt<T> &x) {
  lint a;
  ist >> a;
  x = a;
  return ist;
}
int n, m;
ModInt<> fact[2000010], inv[2000010];
ModInt<> comb(int a, int b) {
  if (a < b)
    return 0;
  return fact[a] * inv[a - b] * inv[b];
}
ModInt<> comb2(int a, int b) { return comb(a + b - 1, b - 1); }
int main() {
  std::cin >> n >> m;
  fact[0] = 1;
  REP(i, 2000000) fact[i] = fact[i - 1] * i;
  inv[2000000] = ModInt<>(1) / fact[2000000];
  for (int i = 1999999; i >= 0; i--)
    inv[i] = inv[i + 1] * (i + 1);
  ModInt<> ans = 0;
  for (int i = m; i >= 0; i -= 2) {
    ans += comb(n, i) * comb2((3 * m - i) / 2, n) -
           (comb(n, i) * comb2((m - i) / 2, n) -
            comb(n - 1, i) * comb2((m - i) / 2, n - 1)) *
               n;
  }
  std::cout << ans << std::endl;
  return 0;
}