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:
/*Lucky_Glass*/
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;

typedef long long ll;
const int N=3e6;
const ll MOD=998244353;

ll Efac[N+3],Einv[N+3];

ll QPow(ll Va,ll Vb){
	ll Rr=1;
	while(Vb){
		if(Vb&1) Rr=Va*Rr%MOD;
		Va=Va*Va%MOD;
		Vb>>=1;
	}
	return Rr;
}
void Process(){
	Efac[0]=1;for(int i=1;i<=N;i++) Efac[i]=Efac[i-1]*i%MOD;
	Einv[N]=QPow(Efac[N],MOD-2);for(int i=N-1;i>=0;i--) Einv[i]=Einv[i+1]*(i+1)%MOD;
}
ll fC(int Va,int Vb){return Efac[Vb]*Einv[Va]%MOD*Einv[Vb-Va]%MOD;}
int main(){
	Process();
	int n,m;scanf("%d%d",&n,&m);
	ll Vans=fC(n-1,3*m+n-1);
	Vans=(Vans-fC(n-1,m+n-2)*n%MOD+MOD)%MOD;
	for(int i=m+1;i<=n && i<=3*m;i++)
		if((3*m-i)%2==0){
			Vans=(Vans-fC(i,n)*fC(n-1,(3*m-i)/2+n-1)%MOD+MOD)%MOD;
		}
	printf("%lld\n",(Vans%MOD+MOD)%MOD);
	return 0;
}