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>
#include <algorithm>
#include <set>
using namespace std;
long long fac[2800100], finv[2800100], inv[2800100]; 
long long MOD = 998244353; 
int MAX = 2800050; 
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;
    }
}
long long 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() { 
	long long int N, M; cin >> N >> M; COMinit();
	long long int ALL = COM(N + M * 3 - 1, N - 1); 
	long long int impo = 0; 
	for(int i = 0; i < M; i++){
		long long int tmp = COM(N + i - 2, i); 
		impo += tmp; impo %= MOD; 
	}
	impo *= N; impo %= MOD;
	long long int impo2 = 0; 
	for(int i = 0; i < M; i++){
		long long int tmp = (COM(N + i - 1, i) * COM(N, 3 * M - i * 2)) % MOD; 
		impo2 += tmp; impo2 %= MOD; 
	}
	cout << (MOD * 2 + ALL - impo - impo2) % MOD << endl; 
}