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 BASE = 998244353;

long long fact[3000300], invFact[3000300];

long long power(long long x, long long y)
{
  if (!y)
    return 1;
  long long res = power(x, y >> 1);
  res = res * res % BASE;
  if (y & 1)
    res = res * x % BASE;
  return res;
}

long long c(int n, int k)
{
  if (k >= n)
    return n == k;
  return fact[n] * invFact[k] % BASE * invFact[n - k] % BASE;
}

int main()
{
  fact[0] = invFact[0] = 1;
  for (int i = 1; i <= 2500000; i++)
  {
    fact[i] = fact[i - 1] * i % BASE;
    invFact[i] = power(fact[i], BASE - 2);
  }

  int n, m;
  cin >> n >> m;

  long long bad = 0;
  // greatest value <= 2m
  for (int i = m * 2 + 1; i <= m * 3; i++)
    bad = (bad + c(m * 3 - i + n - 2, n - 2)) % BASE;
  bad = bad * n % BASE;

  long long ans = 0;
  for (int odd = 0; odd <= min(m, n); odd++)
    if (odd % 2 == m % 2)
    {
      int rem = (m * 3 - odd) / 2;
      ans = (ans + c(rem + n - 1, n - 1) * c(n, odd)) % BASE;
    }

  cout << (ans - bad + BASE) % BASE << endl;
}