Problem p02965 (C++)

Buggy submission (status: Runtime Error):
#ifndef __INTMOD_H__0001__
#define __INTMOD_H__0001__

#include <cassert>
#include <iostream>
#include <vector>

/* Modulus must be less than 0x80000000, and must not be 0. */
template <uint32_t Modulus> class IntMod {
  typedef int Int;
  typedef unsigned int UInt;
  typedef long long Long;
  typedef unsigned long long ULong;

public:
  template <uint32_t Modulus_>
  friend bool operator==(const IntMod<Modulus_> &left,
                         const IntMod<Modulus_> &right);
  template <uint32_t Modulus_>
  friend bool operator!=(const IntMod<Modulus_> &left,
                         const IntMod<Modulus_> &right);
  template <uint32_t Modulus_>
  friend bool operator<(const IntMod<Modulus_> &left,
                        const IntMod<Modulus_> &right);
  template <uint32_t Modulus_>
  friend bool operator<=(const IntMod<Modulus_> &left,
                         const IntMod<Modulus_> &right);
  template <uint32_t Modulus_>
  friend bool operator>(const IntMod<Modulus_> &left,
                        const IntMod<Modulus_> &right);
  template <uint32_t Modulus_>
  friend bool operator>=(const IntMod<Modulus_> &left,
                         const IntMod<Modulus_> &right);

private:
  UInt value_m;

public:
  IntMod() { value_m = 0; }
  IntMod(UInt value) { value_m = value % Modulus; }
  IntMod(ULong value) { value_m = value % Modulus; }
  IntMod(Int value) {
    Int tmp = value % (Int)Modulus;
    value_m = tmp >= 0 ? tmp : Modulus - (unsigned int)(-tmp);
  }
  IntMod(Long value) {
    Int tmp = value % (Long)Modulus;
    value_m = tmp >= 0 ? tmp : Modulus - (unsigned int)(-tmp);
  }
  IntMod(const IntMod &other) : value_m(other.value_m) {}
  IntMod &operator=(const IntMod &other) {
    value_m = other.value_m;
    return *this;
  }

  const IntMod &operator+() const { return *this; }
  IntMod operator-() const { return IntMod(Modulus - value_m); }
  IntMod &operator++() {
    ++value_m;
    if (value_m == Modulus)
      value_m = 0;
    return *this;
  }
  IntMod &operator--() {
    if (value_m == 0)
      value_m = Modulus;
    --value_m;
    return *this;
  }
  IntMod operator++(int dummy) {
    IntMod tmp(*this);
    ++(*this);
    return tmp;
  }
  IntMod operator--(int dummy) {
    IntMod tmp(*this);
    --(*this);
    return tmp;
  }
  IntMod &operator+=(const IntMod &right) {
    value_m += right.value_m; // value_m < 0x80000000
    if (value_m >= Modulus)
      value_m -= Modulus;
    return *this;
  }
  IntMod &operator-=(const IntMod &right) {
    if (value_m < right.value_m)
      value_m += Modulus;
    value_m -= right.value_m;
    return *this;
  }
  IntMod &operator*=(const IntMod &right) {
    value_m = ((ULong)value_m * right.value_m) % Modulus;
    return *this;
  }
  IntMod &operator/=(const IntMod &right) {
    (*this) *= (right.Inverse());
    return *this;
  }
  // for power
  IntMod operator[](ULong exp) const { return Pow(exp); }

  /* Modulus must be a prime. */
  IntMod Inverse() const { return (*this).Pow(Modulus - 2); }
  IntMod Pow(ULong exp) const {
    IntMod product = 1;
    IntMod factor(*this);
    while (exp > 0) {
      if (exp & 1)
        product *= factor;
      factor *= factor;
      exp >>= 1;
    }
    return product;
  }
  UInt Get_value() const { return value_m; }

  static IntMod Fact(UInt num) {
    static std::vector<IntMod> table(1, 1);
    if (table.size() > num)
      return table[num];

    int old_size = table.size();
    table.resize(num + 1);
    for (int i = old_size; i <= num; i++) {
      table[i] = table[i - 1] * i;
    }
    return table[num];
  }

  static IntMod Combi(UInt n, UInt r) {
    if (n < r)
      throw "okashii";
    return IntMod::Fact(n) / (IntMod::Fact(n - r) * IntMod::Fact(r));
  }

  static IntMod Permutation(UInt n, UInt r) {
    if (n < r)
      throw "okashii";
    return IntMod::Fact(n) / IntMod::Fact(n - r);
  }

  static std::vector<IntMod> Inverse_list(int size) {
    assert(size < Modulus);
    std::vector<IntMod> ret_arr(size + 1);
    ret_arr[1] = 1;
    for (int i = 2; i <= size; ++i) {
      ret_arr[i] =
          ((ULong)(Modulus - Modulus / i) * ret_arr[Modulus % i].Get_value()) %
          Modulus;
    }
    return ret_arr;
  }
};

template <uint32_t Modulus>
IntMod<Modulus> operator+(const IntMod<Modulus> &left,
                          const IntMod<Modulus> &right) {
  IntMod<Modulus> ret(left);
  ret += right;
  return ret;
}

template <uint32_t Modulus>
IntMod<Modulus> operator-(const IntMod<Modulus> &left,
                          const IntMod<Modulus> &right) {
  IntMod<Modulus> ret(left);
  ret -= right;
  return ret;
}

template <uint32_t Modulus>
IntMod<Modulus> operator*(const IntMod<Modulus> &left,
                          const IntMod<Modulus> &right) {
  IntMod<Modulus> ret(left);
  ret *= right;
  return ret;
}

template <uint32_t Modulus>
IntMod<Modulus> operator/(const IntMod<Modulus> &left,
                          const IntMod<Modulus> &right) {
  IntMod<Modulus> ret(left);
  ret /= right;
  return ret;
}

template <uint32_t Modulus>
bool operator==(const IntMod<Modulus> &left, const IntMod<Modulus> &right) {
  return left.value_m == right.value_m;
}
template <uint32_t Modulus>
bool operator!=(const IntMod<Modulus> &left, const IntMod<Modulus> &right) {
  return left.value_m != right.value_m;
}
/* for set/map */
template <uint32_t Modulus>
bool operator<(const IntMod<Modulus> &left, const IntMod<Modulus> &right) {
  return left.value_m < right.value_m;
}
template <uint32_t Modulus>
bool operator<=(const IntMod<Modulus> &left, const IntMod<Modulus> &right) {
  return left.value_m <= right.value_m;
}
template <uint32_t Modulus>
bool operator>(const IntMod<Modulus> &left, const IntMod<Modulus> &right) {
  return left.value_m > right.value_m;
}
template <uint32_t Modulus>
bool operator>=(const IntMod<Modulus> &left, const IntMod<Modulus> &right) {
  return left.value_m >= right.value_m;
}

template <uint32_t Modulus, class Integer>
IntMod<Modulus> operator+(const IntMod<Modulus> &left, Integer right) {
  return left + IntMod<Modulus>(right);
}
template <uint32_t Modulus, class Integer>
IntMod<Modulus> operator+(Integer left, const IntMod<Modulus> &right) {
  return IntMod<Modulus>(left) + right;
}
template <uint32_t Modulus, class Integer>
IntMod<Modulus> operator-(const IntMod<Modulus> &left, Integer right) {
  return left - IntMod<Modulus>(right);
}
template <uint32_t Modulus, class Integer>
IntMod<Modulus> operator-(Integer left, const IntMod<Modulus> &right) {
  return IntMod<Modulus>(left) - right;
}
template <uint32_t Modulus, class Integer>
IntMod<Modulus> operator*(const IntMod<Modulus> &left, Integer right) {
  return left * IntMod<Modulus>(right);
}
template <uint32_t Modulus, class Integer>
IntMod<Modulus> operator*(Integer left, const IntMod<Modulus> &right) {
  return IntMod<Modulus>(left) * right;
}
template <uint32_t Modulus, class Integer>
IntMod<Modulus> operator/(const IntMod<Modulus> &left, Integer right) {
  return left / IntMod<Modulus>(right);
}
template <uint32_t Modulus, class Integer>
IntMod<Modulus> operator/(Integer left, const IntMod<Modulus> &right) {
  return IntMod<Modulus>(left) / right;
}

template <uint32_t Modulus>
std::istream &operator<<(std::istream &ist, const IntMod<Modulus> &val) {
  uint64_t tmp;
  ist >> tmp;
  val = tmp;
  return ist;
}

template <uint32_t Modulus>
std::ostream &operator<<(std::ostream &ost, const IntMod<Modulus> &val) {
  ost << val.Get_value();
  return ost;
}

typedef IntMod<1000000007> MInt;

#if 1
MInt operator"" _m(unsigned long long num) { return MInt(num); }
#endif

#endif
#define _CRT_SECURE_NO_WARNINGS
#define _SCL_SECURE_NO_WARNINGS
#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <utility>
#include <valarray>
#include <vector>

using namespace std;
typedef unsigned int uint;
typedef long long LL;
typedef unsigned long long ULL;
typedef pair<LL, LL> PP;
#define REP(i, a, n) for (LL i = (a), i##_max = (n); i < i##_max; ++i)
#define REM(i, a, n) for (LL i = (LL)(n)-1, i##min = (a); i >= i##min; --i)
#define ALL(arr) (arr).begin(), (arr).end()
#define FLOAT fixed << setprecision(16)
#define SPEEDUP                                                                \
  {                                                                            \
    cin.tie(NULL);                                                             \
    ios::sync_with_stdio(false);                                               \
  }
const int INF = 0x3FFFFFFF;
const LL INFLL = 0x3FFFFFFF3FFFFFFF;
const double INFD = 1.0e+308;
const double EPS = 1.0e-9;

void YesNo(bool b) { cout << (b ? "Yes" : "No") << endl; }
void YESNO(bool b) { cout << (b ? "YES" : "NO") << endl; }
template <class T, class U>
istream &operator>>(istream &ist, pair<T, U> &right) {
  return ist >> right.first >> right.second;
}
template <class T, class U>
ostream &operator<<(ostream &ost, const pair<T, U> &right) {
  return ost << right.first << ' ' << right.second;
}
template <class T, class TCompatible, size_t N>
void Fill(T (&dest)[N], const TCompatible &val) {
  fill(dest, dest + N, val);
}
template <class T, class TCompatible, size_t M, size_t N>
void Fill(T (&dest)[M][N], const TCompatible &val) {
  for (int i = 0; i < M; ++i)
    Fill(dest[i], val);
}
template <class T> T Compare(T left, T right) {
  return left > right ? 1 : (left < right ? -1 : 0);
}
istream &Ignore(istream &ist) {
  string s;
  ist >> s;
  return ist;
}
bool Inside(int i, int j, int h, int w) {
  return i >= 0 && i < h && j >= 0 && j < w;
}
template <class T> T Next() {
  T buf;
  cin >> buf;
  return buf;
}

#ifdef ONLY_MY_ENVIR
#include "BIT.h"
#include "BinaryMatrix.h"
#include "Factorization.h"
#include "FlowSolver.h"
#include "Graph.h"
#include "IntMod.h"
#include "LazySegmentTree.h"
#include "Math.h"
#include "Matrix.h"
#include "MinMax.h"
#include "Position.h"
#include "Range.h"
#include "Rational.h"
#include "SegmentTree.h"
#include "SegmentTree2D.h"
#include "SuffixArray.h"
#include "Tree.h"
#include "UnionFind.h"
#endif

#ifdef __GNUC__
typedef __int128 LLL;
istream &operator>>(istream &ist, __int128 &val) {
  LL tmp;
  ist >> tmp;
  val = tmp;
  return ist;
}
ostream &operator<<(ostream &ost, __int128 val) {
  LL tmp = val;
  ost << tmp;
  return ost;
}
#endif

#if 1234567891
#include <array>
#include <random>
#include <unordered_map>
#include <unordered_set>
template <typename T>
using PriorityQ = priority_queue<T, vector<T>, greater<T>>;
// template <class T>
// auto Is(const T& value) { return [value](const auto& comparand) -> bool {
// return comparand == value; }; }
#endif

using MP = IntMod<998244353>;
int N, M;

MP H(int n, int r) { return MP::Combi(n + r - 1, r - 1); }

int main() {
  cin >> N >> M;
  MP ans = H(3 * M, N) - N * MP::Combi(N + M - 2, N - 1);

  REP(i, 0, N + 1) {
    if ((3 * M + i) % 2 == 1)
      continue;
    int even = (3 * M - i) / 2;
    if (even >= i)
      continue;
    ans -= MP::Combi(N, i) * H(even, N);
  }

  cout << ans << endl;
  return 0;
}


Fixed submission:
#ifndef __INTMOD_H__0001__
#define __INTMOD_H__0001__

#include <cassert>
#include <iostream>
#include <vector>

/* Modulus must be less than 0x80000000, and must not be 0. */
template <uint32_t Modulus> class IntMod {
  typedef int Int;
  typedef unsigned int UInt;
  typedef long long Long;
  typedef unsigned long long ULong;

public:
  template <uint32_t Modulus_>
  friend bool operator==(const IntMod<Modulus_> &left,
                         const IntMod<Modulus_> &right);
  template <uint32_t Modulus_>
  friend bool operator!=(const IntMod<Modulus_> &left,
                         const IntMod<Modulus_> &right);
  template <uint32_t Modulus_>
  friend bool operator<(const IntMod<Modulus_> &left,
                        const IntMod<Modulus_> &right);
  template <uint32_t Modulus_>
  friend bool operator<=(const IntMod<Modulus_> &left,
                         const IntMod<Modulus_> &right);
  template <uint32_t Modulus_>
  friend bool operator>(const IntMod<Modulus_> &left,
                        const IntMod<Modulus_> &right);
  template <uint32_t Modulus_>
  friend bool operator>=(const IntMod<Modulus_> &left,
                         const IntMod<Modulus_> &right);

private:
  UInt value_m;

public:
  IntMod() { value_m = 0; }
  IntMod(UInt value) { value_m = value % Modulus; }
  IntMod(ULong value) { value_m = value % Modulus; }
  IntMod(Int value) {
    Int tmp = value % (Int)Modulus;
    value_m = tmp >= 0 ? tmp : Modulus - (unsigned int)(-tmp);
  }
  IntMod(Long value) {
    Int tmp = value % (Long)Modulus;
    value_m = tmp >= 0 ? tmp : Modulus - (unsigned int)(-tmp);
  }
  IntMod(const IntMod &other) : value_m(other.value_m) {}
  IntMod &operator=(const IntMod &other) {
    value_m = other.value_m;
    return *this;
  }

  const IntMod &operator+() const { return *this; }
  IntMod operator-() const { return IntMod(Modulus - value_m); }
  IntMod &operator++() {
    ++value_m;
    if (value_m == Modulus)
      value_m = 0;
    return *this;
  }
  IntMod &operator--() {
    if (value_m == 0)
      value_m = Modulus;
    --value_m;
    return *this;
  }
  IntMod operator++(int dummy) {
    IntMod tmp(*this);
    ++(*this);
    return tmp;
  }
  IntMod operator--(int dummy) {
    IntMod tmp(*this);
    --(*this);
    return tmp;
  }
  IntMod &operator+=(const IntMod &right) {
    value_m += right.value_m; // value_m < 0x80000000
    if (value_m >= Modulus)
      value_m -= Modulus;
    return *this;
  }
  IntMod &operator-=(const IntMod &right) {
    if (value_m < right.value_m)
      value_m += Modulus;
    value_m -= right.value_m;
    return *this;
  }
  IntMod &operator*=(const IntMod &right) {
    value_m = ((ULong)value_m * right.value_m) % Modulus;
    return *this;
  }
  IntMod &operator/=(const IntMod &right) {
    (*this) *= (right.Inverse());
    return *this;
  }
  // for power
  IntMod operator[](ULong exp) const { return Pow(exp); }

  /* Modulus must be a prime. */
  IntMod Inverse() const { return (*this).Pow(Modulus - 2); }
  IntMod Pow(ULong exp) const {
    IntMod product = 1;
    IntMod factor(*this);
    while (exp > 0) {
      if (exp & 1)
        product *= factor;
      factor *= factor;
      exp >>= 1;
    }
    return product;
  }
  UInt Get_value() const { return value_m; }

  static IntMod Fact(UInt num) {
    static std::vector<IntMod> table(1, 1);
    if (table.size() > num)
      return table[num];

    int old_size = table.size();
    table.resize(num + 1);
    for (int i = old_size; i <= num; i++) {
      table[i] = table[i - 1] * i;
    }
    return table[num];
  }

  static IntMod Combi(UInt n, UInt r) {
    if (n < r)
      throw "okashii";
    return IntMod::Fact(n) / (IntMod::Fact(n - r) * IntMod::Fact(r));
  }

  static IntMod Permutation(UInt n, UInt r) {
    if (n < r)
      throw "okashii";
    return IntMod::Fact(n) / IntMod::Fact(n - r);
  }

  static std::vector<IntMod> Inverse_list(int size) {
    assert(size < Modulus);
    std::vector<IntMod> ret_arr(size + 1);
    ret_arr[1] = 1;
    for (int i = 2; i <= size; ++i) {
      ret_arr[i] =
          ((ULong)(Modulus - Modulus / i) * ret_arr[Modulus % i].Get_value()) %
          Modulus;
    }
    return ret_arr;
  }
};

template <uint32_t Modulus>
IntMod<Modulus> operator+(const IntMod<Modulus> &left,
                          const IntMod<Modulus> &right) {
  IntMod<Modulus> ret(left);
  ret += right;
  return ret;
}

template <uint32_t Modulus>
IntMod<Modulus> operator-(const IntMod<Modulus> &left,
                          const IntMod<Modulus> &right) {
  IntMod<Modulus> ret(left);
  ret -= right;
  return ret;
}

template <uint32_t Modulus>
IntMod<Modulus> operator*(const IntMod<Modulus> &left,
                          const IntMod<Modulus> &right) {
  IntMod<Modulus> ret(left);
  ret *= right;
  return ret;
}

template <uint32_t Modulus>
IntMod<Modulus> operator/(const IntMod<Modulus> &left,
                          const IntMod<Modulus> &right) {
  IntMod<Modulus> ret(left);
  ret /= right;
  return ret;
}

template <uint32_t Modulus>
bool operator==(const IntMod<Modulus> &left, const IntMod<Modulus> &right) {
  return left.value_m == right.value_m;
}
template <uint32_t Modulus>
bool operator!=(const IntMod<Modulus> &left, const IntMod<Modulus> &right) {
  return left.value_m != right.value_m;
}
/* for set/map */
template <uint32_t Modulus>
bool operator<(const IntMod<Modulus> &left, const IntMod<Modulus> &right) {
  return left.value_m < right.value_m;
}
template <uint32_t Modulus>
bool operator<=(const IntMod<Modulus> &left, const IntMod<Modulus> &right) {
  return left.value_m <= right.value_m;
}
template <uint32_t Modulus>
bool operator>(const IntMod<Modulus> &left, const IntMod<Modulus> &right) {
  return left.value_m > right.value_m;
}
template <uint32_t Modulus>
bool operator>=(const IntMod<Modulus> &left, const IntMod<Modulus> &right) {
  return left.value_m >= right.value_m;
}

template <uint32_t Modulus, class Integer>
IntMod<Modulus> operator+(const IntMod<Modulus> &left, Integer right) {
  return left + IntMod<Modulus>(right);
}
template <uint32_t Modulus, class Integer>
IntMod<Modulus> operator+(Integer left, const IntMod<Modulus> &right) {
  return IntMod<Modulus>(left) + right;
}
template <uint32_t Modulus, class Integer>
IntMod<Modulus> operator-(const IntMod<Modulus> &left, Integer right) {
  return left - IntMod<Modulus>(right);
}
template <uint32_t Modulus, class Integer>
IntMod<Modulus> operator-(Integer left, const IntMod<Modulus> &right) {
  return IntMod<Modulus>(left) - right;
}
template <uint32_t Modulus, class Integer>
IntMod<Modulus> operator*(const IntMod<Modulus> &left, Integer right) {
  return left * IntMod<Modulus>(right);
}
template <uint32_t Modulus, class Integer>
IntMod<Modulus> operator*(Integer left, const IntMod<Modulus> &right) {
  return IntMod<Modulus>(left) * right;
}
template <uint32_t Modulus, class Integer>
IntMod<Modulus> operator/(const IntMod<Modulus> &left, Integer right) {
  return left / IntMod<Modulus>(right);
}
template <uint32_t Modulus, class Integer>
IntMod<Modulus> operator/(Integer left, const IntMod<Modulus> &right) {
  return IntMod<Modulus>(left) / right;
}

template <uint32_t Modulus>
std::istream &operator<<(std::istream &ist, const IntMod<Modulus> &val) {
  uint64_t tmp;
  ist >> tmp;
  val = tmp;
  return ist;
}

template <uint32_t Modulus>
std::ostream &operator<<(std::ostream &ost, const IntMod<Modulus> &val) {
  ost << val.Get_value();
  return ost;
}

typedef IntMod<1000000007> MInt;

#if 1
MInt operator"" _m(unsigned long long num) { return MInt(num); }
#endif

#endif
#define _CRT_SECURE_NO_WARNINGS
#define _SCL_SECURE_NO_WARNINGS
#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <utility>
#include <valarray>
#include <vector>

using namespace std;
typedef unsigned int uint;
typedef long long LL;
typedef unsigned long long ULL;
typedef pair<LL, LL> PP;
#define REP(i, a, n) for (LL i = (a), i##_max = (n); i < i##_max; ++i)
#define REM(i, a, n) for (LL i = (LL)(n)-1, i##min = (a); i >= i##min; --i)
#define ALL(arr) (arr).begin(), (arr).end()
#define FLOAT fixed << setprecision(16)
#define SPEEDUP                                                                \
  {                                                                            \
    cin.tie(NULL);                                                             \
    ios::sync_with_stdio(false);                                               \
  }
const int INF = 0x3FFFFFFF;
const LL INFLL = 0x3FFFFFFF3FFFFFFF;
const double INFD = 1.0e+308;
const double EPS = 1.0e-9;

void YesNo(bool b) { cout << (b ? "Yes" : "No") << endl; }
void YESNO(bool b) { cout << (b ? "YES" : "NO") << endl; }
template <class T, class U>
istream &operator>>(istream &ist, pair<T, U> &right) {
  return ist >> right.first >> right.second;
}
template <class T, class U>
ostream &operator<<(ostream &ost, const pair<T, U> &right) {
  return ost << right.first << ' ' << right.second;
}
template <class T, class TCompatible, size_t N>
void Fill(T (&dest)[N], const TCompatible &val) {
  fill(dest, dest + N, val);
}
template <class T, class TCompatible, size_t M, size_t N>
void Fill(T (&dest)[M][N], const TCompatible &val) {
  for (int i = 0; i < M; ++i)
    Fill(dest[i], val);
}
template <class T> T Compare(T left, T right) {
  return left > right ? 1 : (left < right ? -1 : 0);
}
istream &Ignore(istream &ist) {
  string s;
  ist >> s;
  return ist;
}
bool Inside(int i, int j, int h, int w) {
  return i >= 0 && i < h && j >= 0 && j < w;
}
template <class T> T Next() {
  T buf;
  cin >> buf;
  return buf;
}

#ifdef ONLY_MY_ENVIR
#include "BIT.h"
#include "BinaryMatrix.h"
#include "Factorization.h"
#include "FlowSolver.h"
#include "Graph.h"
#include "IntMod.h"
#include "LazySegmentTree.h"
#include "Math.h"
#include "Matrix.h"
#include "MinMax.h"
#include "Position.h"
#include "Range.h"
#include "Rational.h"
#include "SegmentTree.h"
#include "SegmentTree2D.h"
#include "SuffixArray.h"
#include "Tree.h"
#include "UnionFind.h"
#endif

#ifdef __GNUC__
typedef __int128 LLL;
istream &operator>>(istream &ist, __int128 &val) {
  LL tmp;
  ist >> tmp;
  val = tmp;
  return ist;
}
ostream &operator<<(ostream &ost, __int128 val) {
  LL tmp = val;
  ost << tmp;
  return ost;
}
#endif

#if 1234567891
#include <array>
#include <random>
#include <unordered_map>
#include <unordered_set>
template <typename T>
using PriorityQ = priority_queue<T, vector<T>, greater<T>>;
// template <class T>
// auto Is(const T& value) { return [value](const auto& comparand) -> bool {
// return comparand == value; }; }
#endif

using MP = IntMod<998244353>;
int N, M;

MP H(int n, int r) { return MP::Combi(n + r - 1, r - 1); }

int main() {
  cin >> N >> M;
  MP ans = H(3 * M, N) - N * MP::Combi(N + M - 2, N - 1);

  REP(i, 0, N + 1) {
    if ((3 * M + i) % 2 == 1)
      continue;
    int even = (3 * M - i) / 2;
    if (even >= i || even < 0)
      continue;
    ans -= MP::Combi(N, i) * H(even, N);
  }

  cout << ans << endl;
  return 0;
}