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 pb push_back
#define mp make_pair
#define fi first
#define se second
#define SZ(x) ((int)x.size())
#define FOR(i,a,b) for (int i=a;i<=b;++i)
#define FORD(i,a,b) for (int i=a;i>=b;--i)
using namespace std;
typedef long long LL;
typedef pair<int,int> pa;
typedef vector<int> vec;
void getint(int &v){
    char ch,fu=0;
    for(ch='*'; (ch<'0'||ch>'9')&&ch!='-'; ch=getchar());
    if(ch=='-') fu=1, ch=getchar();
    for(v=0; ch>='0'&&ch<='9'; ch=getchar()) v=v*10+ch-'0';
    if(fu) v=-v;
}
const int MO=998244353;
int n,m;
LL ans,fac[3000010],inv[3000010];
LL pw(LL x,LL y){
	LL t=1;
	for (;y;y>>=1){
		if (y&1) t=t*x%MO;
		x=x*x%MO;
	}
	return t;
}
LL C(int x,int y){
	return fac[x]*inv[y]%MO*inv[x-y]%MO;
}
int main(){
	fac[0]=1;
	FOR(i,1,3000000) fac[i]=fac[i-1]*i%MO;
	inv[3000000]=pw(fac[3000000],MO-2);
	FORD(i,2999999,0) inv[i]=inv[i+1]*(i+1)%MO;
	cin>>n>>m;
	ans=C(m*3+n-1,n-1);
	(ans-=1ll*n*C(m+n-2,n-1))%=MO;
	FOR(i,m+1,n) if ((m*3-i>=0) && (m*3-i)%2==0) (ans-=C(n,i)*C((m*3-i)/2+n-1,n-1))%=MO;
	ans=(ans%MO+MO)%MO;
	cout<<ans<<endl;
	return 0;
}