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<cstdio>
#include<algorithm>
using namespace std;
const int N=2e6+5;
const int mod=998244353;
int n,m,inv[N],jc[N],jcn[N],foo,bar;
int C(int n,int m){
	if(n<0||m<0||n<m)return 0;
	return 1ll*jc[n]*jcn[m]%mod*jcn[n-m]%mod;
}
int cal(int n,int m){
	return C(n+m-1,n);
}
int main(){
	scanf("%d%d",&n,&m);inv[1]=jc[0]=jcn[0]=1;
	for(int i=2;i<N;++i)inv[i]=1ll*inv[mod%i]*(mod-mod/i)%mod;
	for(int i=1;i<N;++i)jc[i]=1ll*jc[i-1]*i%mod,jcn[i]=1ll*jcn[i-1]*inv[i]%mod;
	for(int i=0;i<=m&&i<=n;++i)if(~(m+m+m-i)&1)foo=(foo+1ll*C(n,i)*cal(m+m+m-i>>1,n))%mod;
	for(int i=0;i<m;++i)bar=(bar+cal(i,n-1))%mod;
	printf("%lld\n",(foo+1ll*(mod-n)*bar)%mod);return 0;
}