Problem: 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.

Examples

Input

2 2


Output

3


Input

3 2


Output

19


Input

10 10


Output

211428932


Input

100000 50000


Output

3463133

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef pair<ll,ll> pll;
typedef vector<bool> vb;
const ll oo = 0x3f3f3f3f3f3f3f3f;
const double eps = 1e-9;
#define sz(c) ll((c).size())
#define all(c) begin(c), end(c)
#define FOR(i,a,b) for (ll i = (a); i < (b); i++)
#define FORD(i,a,b) for (ll i = (b)-1; i >= (a); i--)
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define xx first
#define yy second
#define TR(X) ({ if(1) cerr << "TR: " << (#X) << " = " << (X) << endl; })

const ll N = 5e6 + 10, MOD = 998244353;
ll inv[N], fac[N], inv_fac[N];

void precalc() {
	inv[1] = 1;
	FOR(n,2,N) inv[n] = -(MOD/n)*inv[MOD%n] % MOD;

	fac[0] = 1;
	FOR(n,1,N) fac[n] = n*fac[n-1] % MOD;

	inv_fac[0] = 1;
	FOR(n,1,N) inv_fac[n] = inv[n]*inv_fac[n-1] % MOD;
}

ll binom(ll n, ll k) {
	if (k < 0 || k > n) return 0;
	ll res = fac[n] * inv_fac[k] % MOD * inv_fac[n-k] % MOD;
	if (res < 0) res += MOD;
	return res;
}

int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	
	precalc();

	ll n, m;
	cin >> n >> m;
	
	ll res = binom(3*m+n-1,n-1);
	
	FOR(hmax,2*m+1,3*m+1) {
		res = (res - n*binom(3*m-hmax+n-2,n-2)) % MOD;
	}
	
	FOR(codd,m+1,3*m+1) {
		if (codd%2 != (3*m)%2) continue;
		res = (res - binom(n,codd) * binom((3*m-codd)/2+n-1,n-1)) % MOD;
	}
	
	if (res < 0) res += MOD;
	cout << res << endl;

}