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>
using namespace std;
typedef long long ll;
#define all(x) (x).begin(),(x).end()
const int mod=998244353,MAX=2000005,INF=1<<30;

ll inv[MAX],fac[MAX],finv[MAX];

void make(){
    
    fac[0]=fac[1]=1;
    finv[0]=finv[1]=1;
    inv[1]=1;
    
    for(int i=2;i<MAX;i++){
        inv[i]=mod-inv[mod%i]*(mod/i)%mod;
        fac[i]=fac[i-1]*(ll)i%mod;
        finv[i]=finv[i-1]*inv[i]%mod;
    }
    
}

ll comb(ll a,ll b){
    if(a<b) return 0;
    return fac[a]*(finv[b]*finv[a-b]%mod)%mod;
}

int main(){
    
    make();
    
    int N,M;cin>>N>>M;
    
    ll sum=0;
    
    for(int i=M;i>=0;i-=2){
        if(i>N) continue;
        ll rem=(3*M-i)/2;
        sum+=comb(rem+N-1,N-1)*comb(N,i);
        sum%=mod;
    }
    
    for(int i=M;i>=0;i-=2){
        if(i>N) continue;
        ll rem=(M-i)/2;
        sum+=N*(mod-comb(rem+N-1,N-1))%mod*comb(N,i);
        sum%=mod;
    }
    
    for(int i=M;i>=0;i-=2){
        if(i>N) continue;
        ll rem=(M-i)/2;
        sum+=N*(comb(rem+N-2,N-2))%mod*comb(N-1,i);
        sum%=mod;
    }
    
    cout<<sum<<endl;
    
}