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 For(i,j,k) for (int i=(int)(j);i<=(int)(k);i++)
#define Rep(i,j,k) for (int i=(int)(j);i>=(int)(k);i--)
#define pii pair<int,int>
#define fi first
#define se second
#define PB push_back
#define ll long long
using namespace std;
const int mo=998244353;
const int N=3000005;
int fac[N],inv[N],n,m;
int C(int x,int y){
	if (x<0||y<0||y>x) return 0;
	return 1ll*fac[x]*inv[y]%mo*inv[x-y]%mo;
}
int main(){
	fac[0]=inv[0]=inv[1]=1;
	For(i,2,N-1) inv[i]=1ll*inv[mo%i]*(mo-mo/i)%mo;
	For(i,1,N-1) inv[i]=1ll*inv[i-1]*inv[i]%mo;
	For(i,1,N-1) fac[i]=1ll*fac[i-1]*i%mo;
	int n,m;
	scanf("%d%d",&n,&m);
	int ans=(C(3*m+n-1,n-1)+mo-1ll*C(m-1+n-1,n-1)*n%mo)%mo;
	For(j,m+1,m*3) if ((m*3-j)%2==0)
		ans=(ans+mo-1ll*C(n,j)*C((m*3-j)/2+n-1,n-1)%mo)%mo;
	printf("%d\n",ans);
}