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 itn int
#define all(x) (x).begin(), (x).end()
#define make_unique(x) sort(all((x))); (x).resize(unique(all((x))) - (x).begin())

#define random_shuffle(...) shuffle(__VA_ARGS__, rng)
#define rand() rng()

using namespace std;

inline int nxt() {
	int x;
	scanf("%d", &x);
	return x;
}

const int N = 5111111;
long long fact[N], inv[N], invfact[N];
const int mod = 998244353;

long long C(int n, int k) {
	if (n < k) {
		return 0;
	}
	return fact[n] * invfact[k] % mod * invfact[n - k] % mod;
}

int main() {
	mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

	fact[0] = invfact[0] = 1;
	for (int i = 1; i < N; ++i) {
		inv[i] = (i == 1) ? 1 : mod - inv[mod % i] * (mod / i) % mod;
		fact[i] = fact[i - 1] * i % mod;
		invfact[i] = invfact[i - 1] * inv[i] % mod;
	}

	int n = nxt(), m = nxt();
	long long ans = C(3 * m + n - 1, n - 1) - n * C(m + n - 2, n - 1);

	for (int i = m + 1; i <= n; ++i) {
		if (i % 2 != m % 2) {
			continue;
		}
		long long tmp = C((3 * m - i) / 2 + n - 1, n - 1) * C(n, i) % mod;
		ans -= tmp;
	}

	ans %= mod;
	cout << (ans + mod) % mod << "\n";

	return 0;
}