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;

const int N = 2e6+7, M = 998244353;
LL fac[N], invfac[N];

LL power(LL a, LL p) {
    if (p==0)   return 1;
    LL ans = power(a, p/2);
    ans = (ans*ans)%M;
    if (p%2)    ans = (ans * a)%M;
    return ans;
}

void pre() {
    fac[0] = 1;
    for (int i=1; i<N; i++)
        fac[i] = (fac[i-1]*i)%M;

    invfac[N-1] = power(fac[N-1], M-2);
    for (int i=N-2; i>=0; i--)
        invfac[i] = (invfac[i+1] * (i+1))%M;
}

LL C(int n, int k) {
    if (k<0 || k>n) return 0;
    LL denom = (invfac[k]*invfac[n-k])%M;
    return (fac[n]*denom)%M;
}

int main() {
    pre();
    int n, m;
    cin>>n>>m;

    LL ans = 0;
    for (int i=0; i<=n && i<=m; i++) {
        LL choose = C(n, i);
        LL rem = 3*m - i;
        if (rem%2)  continue;
        rem/=2;

        LL ways = C(rem+n-1,n-1);
        LL bad = ((n-i)*C(rem-m-1+n-1,n-1) + i*C(rem-m+n-1, n-1))%M;

//        cout<<i<<" "<<ways<<" "<<bad<<endl;
        ways = (ways-bad+M)%M;

//        cout<<i<<" "<<ways<<endl;
        ans = (ans + ways*choose)%M;
    }
    cout<<ans<<endl;
}