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:
#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math")
#include <bits/stdc++.h>
using namespace std;
template<class t> inline t read(t &x){
	char c=getchar();bool f=0;x=0;
	while(!isdigit(c)) f|=c=='-',c=getchar();
	while(isdigit(c)) x=(x<<1)+(x<<3)+(c^48),c=getchar();
	if(f) x=-x;return x;
}
template<class t,class ...A> inline void read(t &x,A &...a){
	read(x);read(a...);
}
template<class t> inline void write(t x){
	if(x<0) putchar('-'),write(-x);
	else{if(x>9) write(x/10);putchar('0'+x%10);}
}

#define int long long

const int mod=998244353,N=3e6+5;
int n,m,fac[N],inv[N],ans;

int fpow(int x,int y){
	int res=1;
	for(;y;y>>=1,x=x*x%mod) if(y&1) res=res*x%mod;
	return res;
}

int C(int n,int m){
	if(n<m||m<0) return 0;
	return fac[n]*inv[m]%mod*inv[n-m]%mod;
}

int calc(int m){
	return C(n+m-1,n-1);
}

void init(int n){
	fac[0]=1;for(int i=1;i<=n;i++) fac[i]=fac[i-1]*i%mod;
	inv[n]=fpow(fac[n],mod-2);for(int i=n-1;~i;i--) inv[i]=inv[i+1]*(i+1)%mod;
}

signed main(){
	read(n,m);
	init(3e6);
	for(int i=0;i<=n&&i<=m;i++) if(~i&1^m&1){
		ans=(ans+C(n,i)*calc((3*m-i)/2))%mod;
		ans=(ans-C(n-1,i)*n%mod*calc((m-i-2)/2))%mod;
		ans=(ans-C(n-1,i-1)*n%mod*calc((m-i)/2))%mod;
	}
	write((ans+mod)%mod);
}