Problem:
Score : 900 points

Problem Statement

We have a sequence of N integers: x=(x_0,x_1,\cdots,x_{N-1}).
Initially, x_i=0 for each i (0 \leq i \leq N-1).

Snuke will perform the following operation exactly M times:

Choose two distinct indices i, j (0 \leq i,j \leq N-1,\ i \neq j).
Then, replace x_i with x_i+2 and x_j with x_j+1.

Find the number of different sequences that can result after M operations.
Since it can be enormous, compute the count modulo 998244353.

Constraints

2 \leq N \leq 10^6

1 \leq M \leq 5 \times 10^5

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M

Output

Print the number of different sequences that can result after M operations, modulo 998244353.

Sample Input 1

2 2

Sample Output 1

3

After two operations, there are three possible outcomes:

x=(2,4)

x=(3,3)

x=(4,2)

For example, x=(3,3) can result after the following sequence of operations:

First, choose i=0,j=1, changing x from (0,0) to (2,1).

Second, choose i=1,j=0, changing x from (2,1) to (3,3).

Sample Input 2

3 2

Sample Output 2

19

Sample Input 3

10 10

Sample Output 3

211428932

Sample Input 4

100000 50000

Sample Output 4

3463133

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
#ifndef ONLINE_JUDGE
	#include <boost/multiprecision/cpp_int.hpp>
	#include <boost/multiprecision/cpp_dec_float.hpp>
	using bll = boost::multiprecision::cpp_int;
	using bdouble = boost::multiprecision::cpp_dec_float_100;
#endif
#ifdef LOCAL_DEV
	void debug_impl() { std::cerr << '\n'; }
	template<typename Head, typename... Tail> void debug_impl(Head head, Tail... tail) { std::cerr << " " << head << (sizeof...(tail) ? "," : ""); debug_impl(tail...); }
	#define debug(...) do { std::cerr << "(" << #__VA_ARGS__ << ") ="; debug_impl(__VA_ARGS__); } while (false)
#else
	#define debug(...) do {} while (false)
#endif
#ifdef LOCAL_TEST
	#define BOOST_STACKTRACE_USE_ADDR2LINE
	#define BOOST_STACKTRACE_ADDR2LINE_LOCATION /usr/local/opt/binutils/bin/addr2line
	#define _GNU_SOURCE
	#include <boost/stacktrace.hpp>
	namespace std {
		template<typename T> class dvector : public std::vector<T> {
		public:
			dvector() : std::vector<T>() {}
			explicit dvector(size_t n, const T& value = T()) : std::vector<T>(n, value) {}
			dvector(const std::vector<T>& v) : std::vector<T>(v) {}
			dvector(const std::initializer_list<T> il) : std::vector<T>(il) {}
			dvector(const typename std::vector<T>::iterator first, const typename std::vector<T>::iterator last) : std::vector<T>(first, last) {}
			dvector(const std::string::iterator first, const std::string::iterator last) : std::vector<T>(first, last) {}
			T& operator[](size_t n) {
				try { return this->at(n); } catch (const std::exception& e) {
					std::cerr << boost::stacktrace::stacktrace() << '\n'; return this->at(n);
				}
			}
			const T& operator[](size_t n) const {
				try { return this->at(n); } catch (const std::exception& e) {
					std::cerr << boost::stacktrace::stacktrace() << '\n'; return this->at(n);
				}
			}
		};
	}
	class dbool {
	private:
		bool boolvalue;
	public:
		dbool() : boolvalue(false) {}
		dbool(bool b) : boolvalue(b) {}
		dbool(const dbool& b) : boolvalue(b.boolvalue) {}
		operator bool&() { return boolvalue; }
		operator const bool&() const { return boolvalue; }
	};
	template<typename T> std::ostream& operator<<(std::ostream& s, const std::dvector<T>& v) {
		for (size_t i = 0; i < v.size(); ++i){ s << v[i]; if (i < v.size() - 1) s << "\t"; } return s; }
	template<typename T> std::ostream& operator<<(std::ostream& s, const std::dvector<std::dvector<T>>& vv) {
		s << "\n"; for (size_t i = 0; i < vv.size(); ++i){ s << vv[i] << "\n"; } return s; }
	template<typename T> std::ostream& operator<<(std::ostream& s, const std::set<T>& se) {
		s << "{ "; for (auto itr = se.begin(); itr != se.end(); ++itr){ s << (*itr) << "\t"; } s << "}"; return s; }
	template<typename T> std::ostream& operator<<(std::ostream& s, const std::multiset<T>& se) {
		s << "{ "; for (auto itr = se.begin(); itr != se.end(); ++itr){ s << (*itr) << "\t"; } s << "}"; return s; }
	template <typename T, size_t N> std::ostream& operator<<(std::ostream& s, const std::array<T, N>& a) {
		s << "{ "; for (size_t i = 0; i < N; ++i){ s << a[i] << "\t"; } s << "}"; return s; }
	template<typename T1, typename T2> std::ostream& operator<<(std::ostream& s, const std::map<T1, T2>& m) {
		s << "{\n"; for (auto itr = m.begin(); itr != m.end(); ++itr){ s << "\t" << (*itr).first << " : " << (*itr).second << "\n"; } s << "}"; return s; }
	template<typename T1, typename T2> std::ostream& operator<<(std::ostream& s, const std::pair<T1, T2>& p) {
		return s << "(" << p.first << ", " << p.second << ")"; }
	#define vector dvector
	#define bool dbool
	class SIGFPE_exception : std::exception {};
	class SIGSEGV_exception : std::exception {};
	void catch_SIGFPE(int e) { std::cerr << boost::stacktrace::stacktrace() << '\n'; throw SIGFPE_exception();	}
	void catch_SIGSEGV(int e) { std::cerr << boost::stacktrace::stacktrace() << '\n'; throw SIGSEGV_exception(); }
	signed convertedmain();
	signed main() { signal(SIGFPE, catch_SIGFPE); signal(SIGSEGV, catch_SIGSEGV); return convertedmain(); }
	#define main() convertedmain()
#endif
//#define int long long
using ll = long long;
//constexpr int INF = 1e9;//INT_MAX=(1<<31)-1=2147483647
constexpr ll INF = (ll)1e18;//(1LL<<63)-1=9223372036854775807
constexpr ll MOD = 998244353;//(ll)1e9 + 7;
constexpr double EPS = 1e-9;
constexpr ll dx[4] = {1LL, 0LL, -1LL, 0LL};
constexpr ll dy[4] = {0LL, 1LL, 0LL, -1LL};
constexpr ll dx8[8] = {1LL, 0LL, -1LL, 0LL, 1LL, 1LL, -1LL, -1LL};
constexpr ll dy8[8] = {0LL, 1LL, 0LL, -1LL, 1LL, -1LL, 1LL, -1LL};
#define rep(i, n)   for(ll i=0, i##_length=(n); i< i##_length; ++i)
#define repeq(i, n) for(ll i=1, i##_length=(n); i<=i##_length; ++i)
#define rrep(i, n)   for(ll i=(n)-1; i>=0; --i)
#define rrepeq(i, n) for(ll i=(n)  ; i>=1; --i)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
void p() { std::cout << '\n'; }
template<typename Head, typename... Tail> void p(Head head, Tail... tail) { std::cout << head << (sizeof...(tail) ? " " : ""); p(tail...); }
template<typename T> inline void pv(std::vector<T>& v) { for(ll i=0, N=v.size(); i<N; i++) std::cout << v[i] << " \n"[i==N-1]; }
template<typename T> inline T gcd(T a, T b) { return b ? gcd(b,a%b) : a; }
template<typename T> inline T lcm(T a, T b) { return a / gcd(a,  b) * b; }
template<typename T> inline bool chmax(T& a, T b) { return a < b && (a = b, true); }
template<typename T> inline bool chmin(T& a, T b) { return a > b && (a = b, true); }
template<typename T> inline void uniq(std::vector<T>& v) { v.erase(std::unique(v.begin(), v.end()), v.end()); }

/*-----8<-----template-----8<-----*/

inline constexpr ll extgcd(ll a, ll b, ll &x, ll &y){ ll g = a; x = 1; y = 0; if(b){ g = extgcd(b, a % b, y, x); y -= a / b * x; } return g; }
inline constexpr ll invmod(ll a, ll m = MOD){ ll x = 0, y = 0; extgcd(a, m, x, y); return (x + m) % m; }
class Modint{
public:
	ll _num;
	constexpr Modint() : _num() { _num = 0; }
	constexpr Modint(ll x) : _num() { _num = x % MOD; if(_num < 0) _num += MOD; }
	inline constexpr Modint operator= (int x){ _num = x % MOD; if(_num<0) _num += MOD; return *this; }
	inline constexpr Modint operator= (ll x){ _num = x % MOD; if(_num<0) _num += MOD; return *this; }
	inline constexpr Modint operator= (Modint x){ _num = x._num; return *this; }
	inline constexpr Modint operator+ (int x){ return Modint(_num + x); }
	inline constexpr Modint operator+ (ll x){ return Modint(_num + x); }
	inline constexpr Modint operator+ (Modint x){ ll a = _num + x._num; if(a >= MOD) a -= MOD; return Modint{a}; }
	inline constexpr Modint operator+=(int x){ _num += x; _num %= MOD; if(_num < 0) _num += MOD; return *this; }
	inline constexpr Modint operator+=(ll x){ _num += x; _num %= MOD; if(_num < 0) _num += MOD; return *this; }
	inline constexpr Modint operator+=(Modint x){ _num += x._num; if(_num >= MOD) _num -= MOD; return *this; }
	inline constexpr Modint operator++(){ _num++; if(_num == MOD) _num = 0; return *this; }
	inline constexpr Modint operator- (int x){ return Modint(_num - x); }
	inline constexpr Modint operator- (ll x){ return Modint(_num - x); }
	inline constexpr Modint operator- (Modint x){ ll a = _num - x._num; if(a < 0) a += MOD; return Modint{a}; }
	inline constexpr Modint operator-=(int x){ _num -= x; _num %= MOD; if(_num < 0) _num += MOD; return *this; }
	inline constexpr Modint operator-=(ll x){ _num -= x; _num %= MOD; if(_num < 0) _num += MOD; return *this; }
	inline constexpr Modint operator-=(Modint x){ _num -= x._num; if(_num < 0) _num += MOD; return *this; }
	inline constexpr Modint operator--(){ _num--; if(_num == -1) _num = MOD - 1; return *this; }
	inline constexpr Modint operator* (int x){ return Modint(_num * (x % MOD)); }
	inline constexpr Modint operator* (ll x){ return Modint(_num * (x % MOD)); }
	inline constexpr Modint operator* (Modint x){ return Modint{_num * x._num % MOD}; }
	inline constexpr Modint operator*=(int x){ _num *= Modint(x); _num %= MOD; return *this; }
	inline constexpr Modint operator*=(ll x){ _num *= Modint(x); _num %= MOD; return *this; }
	inline constexpr Modint operator*=(Modint x){ _num *= x._num; _num %= MOD; return *this; }
	inline constexpr Modint operator/ (int x){ return Modint(_num * invmod(Modint(x), MOD)); }
	inline constexpr Modint operator/ (ll x){ return Modint(_num * invmod(Modint(x), MOD)); }
	inline constexpr Modint operator/ (Modint x){ return Modint{_num * invmod(x._num, MOD) % MOD}; }
	inline constexpr Modint operator/=(int x){ _num *= invmod(Modint(x), MOD); _num %= MOD; return *this; }
	inline constexpr Modint operator/=(ll x){ _num *= invmod(Modint(x), MOD); _num %= MOD; return *this; }
	inline constexpr Modint operator/=(Modint x){ _num *= invmod(x._num, MOD); _num %= MOD; return *this; }
	inline constexpr Modint pow(ll n){ ll i = 1, x = n>=0 ? n : -n; Modint ans = 1, cnt = n>=0 ? *this : Modint(1) / *this; while(i <= x){ if(x & i){ ans *= cnt; x ^= i; } cnt *= cnt; i *= 2; } return ans; }
	inline constexpr operator ll() const { return _num; }
};
inline std::istream& operator>>(std::istream &s, Modint &x){ ll t; s>>t; x=t; return s; }
vector<Modint> fac(1, 1), inv(1, 1);
inline void reserve(size_t a){
	if(fac.size() >= a) return;
	if(a < fac.size() * 2) a = fac.size() * 2;
	if(a >= MOD) a = MOD;
	while(fac.size() < a) fac.push_back(fac.back() * ll(fac.size()));
	inv.resize(fac.size());
	inv.back() = Modint(1) / fac.back();
	for(ll i = inv.size() - 1; !inv[i - 1]; i--) inv[i - 1] = inv[i] * i;
}
inline Modint factorial(ll n){ if(n < 0) return 0; reserve(n + 1); return fac[n]; }
inline Modint nPk_loop(ll n, ll k){ if(n<k) return 0; Modint val(1); for(ll i=n;i>(n-k);i--)val*=i; return val; }
inline Modint nCk_loop(ll n, ll k){ if(n<k) return 0; Modint val(1); k=min(k,n-k); for(ll i=n;i>(n-k);i--)val*=i; for(ll i=k;i>1;i--)val/=i; return val; };
inline Modint nPk(ll n, ll k){ if(k < 0 || n < k) return 0; if(n>=(ll)1e7) return nPk_loop(n, k); reserve(n + 1); return fac[n] * inv[n - k]; }
inline Modint nCk(ll n, ll k){ if(k < 0 || n < k) return 0; if(n>=(ll)1e7) return nCk_loop(n, k); reserve(n + 1); return fac[n] * inv[k] * inv[n - k]; }
inline Modint nHk(ll n, ll k){ return nCk(n + k - 1, k); } //n種類のものから重複を許してk個選ぶ=玉k個と仕切りn-1個

/*
nCk：n!が間に合わないくらい巨大でkが小さいとき、素直に計算すると間に合う のは1e7以上に組み込んであります
	auto f = [](ll n, ll k){
		if(n<k)return Modint(0);
		Modint val(1);
		k=min(k,n-k);
		for(ll i=n;i>(n-k);i--)val*=i;
		for(ll i=k;i>1;i--)val/=i;
		return val;
	};
*/


//区間add, 区間sum ができる
template< typename T >
class BinaryIndexedTree {
public:
	class BinaryIndexedTreeNaive {
	public:
		ll size;
		vector<T> data;
		BinaryIndexedTreeNaive(ll N) : size(N+1), data(size, 0) {}

		// sum [0, i)
		T sum(ll i) {
			T ret = 0;
			for(--i; i>=0; i=(i&(i+1))-1) ret += data[i];
			return ret;
		}

		// sum [i, j)
		T sum(ll i, ll j) {
			return sum(j) - sum(i);
		}

		// add x to i
		void add(ll i, T x) {
			for(; i < size; i|=i+1) data[i] += x;
		}
	};
	ll size;
	BinaryIndexedTreeNaive b,c;
	BinaryIndexedTree(ll N) : size(N), b(size), c(size) {}

	// add x to [i, j) 
	void add(ll i, ll j, T x) {
		b.add(i,x*-i);
		b.add(j,x*j);
		c.add(i,x);
		c.add(j,x*-1);
	}

	// sum [0, i)
	T sum(ll i) { 
		return b.sum(i+1) + c.sum(i+1)*i;
	}

	// sum [i, j)
	T sum(ll i, ll j) {
		return sum(j) - sum(i);
	}
};
template<typename T> std::ostream& operator<<(std::ostream& s, BinaryIndexedTree<T>& bit) { 
	for(ll i=0; i<bit.size; i++) s << bit.sum(i, i+1) << "\t\n"[i==bit.size-1];
	return s;
}

/*-----8<-----library-----8<-----*/

void solve() {
	ll N,M;
	cin>>N>>M;
	//単純に3M点をN人に配る
	Modint ans=nCk(3*M + N-1, N-1);

	//違反1 ある一人が[2M+1,3M]点取ってしまっている
	Modint t=0;
	for(ll i=2*M+1; i<=3*M; i++){
		t+=nCk(3*M-i + N-2, N-2)*N;
	}

	//違反2 2点獲得した回数が[0,M-1]回しかない
	Modint s=0;
	for(ll i=0; i<=M-1; i++){
		//2点*i個をN人に配る　x 残り 3M-2i点を1点ずつ3M-2i人に配る
		s+=nCk(i + N-1, N-1)*nCk(N, 3*M-2*i);
	}

	debug(ans,t,s);
	ans-=t+s;
	p(ans);
}

signed main() {
	solve();
	return 0;
}