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 MOD 998244353

using namespace std;

typedef long long ll;

ll pow_mod(ll x,int k) {
  ll ans=1;
  while (k) {
  	if (k&1) ans=ans*x%MOD;
  	x=x*x%MOD;
  	k>>=1;
  }
  return ans;
}

ll facd[3000005],facv[3000005];

void pre(int n) {
  facd[0]=1;
  for(int i=1;i<=n;i++) facd[i]=facd[i-1]*i%MOD;
  facv[n]=pow_mod(facd[n],MOD-2);
  for(int i=n-1;i>=0;i--) facv[i]=facv[i+1]*(i+1)%MOD;
}

inline ll C(int n,int m) {
  return (n<m)?0:facd[n]*facv[m]%MOD*facv[n-m]%MOD;
}

int main() {
  int n,m;
  scanf("%d%d",&n,&m);
  pre(n+3*m);
  int ans=C(n+3*m-1,n-1);
  ans=(ans-n*C(n+m-2,n-1)%MOD+MOD)%MOD;
  for(int i=m+2;i<=n;i+=2)
    ans=(ans-C(n,i)*C(n+((3*m-i)>>1)-1,n-1)%MOD+MOD)%MOD;
  printf("%d\n",ans);
  return 0;
}