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>
#define MO 998244353
typedef long long ll;
const int maxn = 3000000;

ll n,m,ans;
ll inv[maxn],fac[maxn];

ll C(ll n, ll m)
{
	if (n < m) return 0;
	return fac[n]*inv[m]%MO*inv[n-m]%MO;
}
ll f(ll n, ll m, ll k)
{
	ll ret = 0;
	for (ll p=0; p<=k; p++)
		if (((m-p)&1)==0){
			ret = (ret+C((m-p)/2ll+n-1, n-1)*C(n, p)%MO)%MO;
		}
	return ret;
}
int main()
{
	scanf("%lld%lld",&n,&m);
	fac[0] = inv[0] = inv[1] = 1;
	for (int i=2; i<=n+3*m; i++)
		inv[i] = (MO-1ll*MO/i*inv[MO%i]%MO);
	for (int i=1; i<=n+3*m; i++)
		inv[i] = inv[i-1]*inv[i]%MO, fac[i] = fac[i-1]*i%MO;
	ans = (f(n, 3*m, m)-n*(f(n, m-1, m))%MO+MO)%MO;
	printf("%lld\n",ans);
	return 0;
}