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<iostream>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<vector>
#include<map>
#include<set>
#include<string>
#include<queue>
#include<stack>
using namespace std;
#define MOD 998244353
#define INF (1<<29)
#define LINF (1LL<<60)
#define EPS (1e-10)
typedef long long Int;
typedef pair<Int, Int> P;

Int fact[3240000];
Int revfact[3240000];
Int rev[3240000];

void init(){
    Int m = MOD;
    fact[0] = 1;
    revfact[0] = 1;
    rev[0] = 0;
    rev[1] = 1;
    for(int i = 1;i < 3240000;i++){
        fact[i] = fact[i-1] * i % m;
        if(i>1)rev[i] = MOD / i * (MOD-rev[MOD % i]) % MOD;
        revfact[i] = revfact[i-1] * rev[i] % MOD;
    }
}

Int nCk(Int n, Int k){
    if(n < k)return 0;
    return fact[n] * revfact[n-k] % MOD * revfact[k] % MOD;
}

Int res;
Int n, m;
int main(){
    init();
    cin >> n >> m;
    res = nCk(3*m + n - 1, n - 1);
    res -= n * nCk(m - 1 + n - 1, n - 1) % MOD;
    for(int i = m+1;i <= n && i <= 3 * m;i++){
        if((3 * m - i) % 2)continue;
        int rest = (3 * m - i) / 2;
        res -= nCk(n, i) * nCk(rest + n - 1, n - 1) % MOD;
        res %= MOD;
    }
    if(res < 0)res += MOD;
    cout << res << endl;
    return 0;
}