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 rep(i,n) for (int i = 0; i < n; i++)
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> pi;
typedef pair<pi, pi> pp;
typedef pair<ll, ll> pl;
const double EPS = 1e-9;
const ll MOD = 998244353;
const int inf = 1 << 30;
const ll linf = 1LL << 60;
const double PI = 3.14159265358979323846;

ll kai[2000001];
ll mokai[2000001];

ll mod_pow (ll x, ll y) {
    ll ret = 1;
    while (y) {
        if (y&1) ret = ret*x%MOD;
        x = x*x%MOD;
        y /= 2;
    }
    return ret;
}

void init (int _n) {
    kai[0] = 1;
    for (int i = 1; i <= _n; i++) kai[i] = kai[i-1]*i%MOD;
    for (int i = 0; i <= _n; i++) mokai[i] = mod_pow(kai[i],MOD-2);
}

ll conb (ll x, ll y) {
    ll z = x-y;
    ll ret = kai[x]*mokai[y]%MOD;
    ret = ret*mokai[z]%MOD;
    return ret;
}

ll n, m;

int main() {
    init(2000000);
    cin >> n >> m;
    ll ans = 0;
    for (int i = m%2; i <= min(n,m); i += 2) {
        ll M = m + (m-i)/2;
        ans = (ans + conb(n-1+M, n-1) * conb(n, i)) % MOD;
    }
    ans = (ans - n * (conb(n-1+m-1, n-1)+MOD) + MOD*MOD) % MOD;
    cout << ans << endl;
}