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;
using Int = long long;
const int MAX = 2000000;
const int MOD = 998244353;
Int fac[MAX], finv[MAX], inv[MAX];
void COMinit() {
    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    inv[1] = 1;
    for (int i = 2; i < MAX; i++){
        fac[i] = fac[i - 1] * i % MOD;
        inv[i] = MOD - inv[MOD%i] * (MOD / i) % MOD;
        finv[i] = finv[i - 1] * inv[i] % MOD;
    }
}
Int COM(int n, int k){
    if (n < k) return 0;
    if (n < 0 || k < 0) return 0;
    return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}
int main()
{
    COMinit();
    int N, M; cin >> N >> M;
    Int a = 0, b = 0, c = 0;
    for (int o = M % 2; o <= M; o += 2) {
        int t = (3 * M - o) / 2;
        a += COM(t + N - 1, N - 1) * COM(N, o);
        a %= MOD;
    }
    for (int o = M % 2; o <= M; o += 2) {
        int t = (3 * M - o) / 2;
        b += N * COM((t - M) + N - 1, N - 1) % MOD * COM(N - 1, o - 1);
        b %= MOD;
    }
    for (int o = M % 2; o <= M; o += 2) {
        int t = (3 * M - o) / 2;
        c += N * COM((t - M - 1) + N - 1, N - 1) % MOD * COM(N - 1, o);
        c %= MOD;
    }
    cout << (a + MOD - b + MOD - c) % MOD << '\n';
    return 0;
}