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;

const int maxn = 2.5e6, mod = 998244353;
int n, m, k, fact[maxn + 3], finv[maxn + 3];

int qpow(int a, int b) {
	int c = 1;
	for (; b; b >>= 1, a = 1ll * a * a % mod) {
		if (b & 1) c = 1ll * a * c % mod;
	}
	return c;
}

void prework(int n) {
	fact[0] = 1;
	for (int i = 1; i <= n; i++) {
		fact[i] = 1ll * fact[i - 1] * i % mod;
	}
	finv[n] = qpow(fact[n], mod - 2);
	for (int i = n; i; i--) {
		finv[i - 1] = 1ll * finv[i] * i % mod;
	}
}

int C(int n, int m) {
	if (n < 0 || m < 0 || m > n) {
		return 0;
	}
	return 1ll * fact[n] * finv[m] % mod * finv[n - m] % mod;
}

int main() {
	scanf("%d %d", &n, &m);
	k = n + 1.5 * m;
	prework(k);
	int ans = 0;
	for (int i = 0; i <= m; i++) {
		if ((m * 3 - i) & 1) continue;
		int t = (m * 3 - i) >> 1;
		ans = (ans + 1ll * C(n, i) * C(t + n - 1, n - 1)) % mod;
	}
	ans = (ans + 1ll * mod * mod - 1ll * n * C(m - 1 + n - 1, n - 1)) % mod;
	printf("%d\n", ans);
	return 0;
}