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;

#define fi first
#define se second
#define mp make_pair
#define pb push_back
#define eb emplace_back

typedef long long ll;
typedef pair<int, int> pi;

int n;
int m;

const int mod = 998244353;
const int maxn = 5e6 + 5;

int fac[maxn], inv[maxn];

int qpow(int a, int n){
    int ret = 1;
    while(n > 0){
        if(n & 1){
            ret = 1LL * ret * a % mod;
        }
        a = 1LL * a * a % mod;
        n >>= 1;
    }
    return ret;
}

void pre_comb(){
    fac[0] = 1;
    for(int i = 1;i < maxn;i++){
        fac[i] = 1LL * fac[i - 1] * i % mod;
    }
    inv[maxn - 1] = qpow(fac[maxn - 1], mod - 2);
    for(int i = maxn - 2;i >= 0;i--){
        inv[i] = 1LL * inv[i + 1] * (i + 1) % mod;
    }
}

int comb(int n, int m){
    if(m > n or m < 0) return 0;
    return 1LL * fac[n] * inv[m] % mod * inv[n - m] % mod;
}

int solve(int m, int n, int b){
    int ret = 0;
    for(int a = 0;a <= b;a++){
        if((m - a) & 1)
            continue;
        ret = (ret + 1LL * comb(n, a) * comb((m - a) / 2 + n - 1, n - 1)) % mod;
    }
    return ret;
}

int main(){
    ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
    pre_comb();
    cin >> n >> m;
    int ans = solve(m * 3, n, m);
    int tmp = (solve(m, n, m) - solve(m, n - 1, m) + mod) % mod;
    tmp = 1LL * n * tmp % mod;
    ans = (ans - tmp + mod) % mod;
    cout << ans << endl;
    return 0;
}