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 PYTHON3):

Solution:
from functools import lru_cache


def prepare(n, MOD):
    f = 1
    factorials = [1]
    for m in range(1, n + 1):
        f *= m
        f %= MOD
        factorials.append(f)
    inv = pow(f, MOD - 2, MOD)
    invs = [1] * (n + 1)
    invs[n] = inv
    for m in range(n, 1, -1):
        inv *= m
        inv %= MOD
        invs[m - 1] = inv

    return factorials, invs


def get_nhr(n, facts, invs):
    @lru_cache(maxsize=None)
    def nhr(r):
        return facts[n + r - 1] * invs[r] * invs[n - 1] % MOD

    return nhr


MOD = 998244353
n, m = list(map(int, input().split()))
facts, invs = prepare(n + 3 * m, MOD)
nhr = get_nhr(n, facts, invs)
ans = 0
for odd in range(m % 2, min(m, n) + 1, 2):
    tmp = nhr((3 * m - odd) // 2)
    if odd > 0:
        tmp -= odd * nhr((m - odd) // 2)
    if odd < n and odd <= m - 2:
        tmp -= (n - odd) * nhr((m - odd - 2) // 2)
    ans = (ans + facts[n] * invs[odd] * invs[n - odd] % MOD * tmp) % MOD
print(ans)