#include <cstdio>
#include <algorithm>
using namespace std;

const int Maxn = 3e6;
const int Mod = 998244353;

int fac[Maxn + 5], inv_fac[Maxn + 5];
inline int QuickPow(int a, int k) {
	int ret = 1;
	while(k) {
		if(k & 1)
			ret = 1LL * ret * a % Mod;
		a = 1LL * a * a % Mod;
		k >>= 1;
	}
	return ret;
}
void Init() {
	fac[0] = inv_fac[0] = 1;
	for(int i = 1; i <= Maxn; i++)
		fac[i] = 1LL * fac[i - 1] * i % Mod;
	inv_fac[Maxn] = QuickPow(fac[Maxn], Mod - 2);
	for(int i = Maxn - 1; i > 0; i--)
		inv_fac[i] = 1LL * inv_fac[i + 1] * (i + 1) % Mod;
}
inline int C(int n, int m) {
	return 1LL * fac[n] * inv_fac[m] % Mod * inv_fac[n - m] % Mod;
}

int main() {
#ifdef LOACL
	freopen("in.txt", "r", stdin);
	freopen("out.txt", "w", stdout);
#endif
	Init();
	int N, M;
	scanf("%d %d", &N, &M);
	int ans = C(3 * M + N - 1, N - 1);
	ans = (ans - 1LL * C(M + N - 2, N - 1) * N % Mod + Mod) % Mod;
	for(int i = M + 1; i <= N && i <= 3 * M; i++)
		if((3 * M - i) % 2 == 0)
			ans = (ans - (1LL * C(N, i) * C((3 * M - i) / 2 + N - 1, N - 1) % Mod) + Mod) % Mod;
	printf("%d\n", ans);
	return 0;
}
### Prompt

Create a solution in Cpp for the following 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

### Response

```cpp
#include <cstdio>
#include <algorithm>
using namespace std;

const int Maxn = 3e6;
const int Mod = 998244353;

int fac[Maxn + 5], inv_fac[Maxn + 5];
inline int QuickPow(int a, int k) {
	int ret = 1;
	while(k) {
		if(k & 1)
			ret = 1LL * ret * a % Mod;
		a = 1LL * a * a % Mod;
		k >>= 1;
	}
	return ret;
}
void Init() {
	fac[0] = inv_fac[0] = 1;
	for(int i = 1; i <= Maxn; i++)
		fac[i] = 1LL * fac[i - 1] * i % Mod;
	inv_fac[Maxn] = QuickPow(fac[Maxn], Mod - 2);
	for(int i = Maxn - 1; i > 0; i--)
		inv_fac[i] = 1LL * inv_fac[i + 1] * (i + 1) % Mod;
}
inline int C(int n, int m) {
	return 1LL * fac[n] * inv_fac[m] % Mod * inv_fac[n - m] % Mod;
}

int main() {
#ifdef LOACL
	freopen("in.txt", "r", stdin);
	freopen("out.txt", "w", stdout);
#endif
	Init();
	int N, M;
	scanf("%d %d", &N, &M);
	int ans = C(3 * M + N - 1, N - 1);
	ans = (ans - 1LL * C(M + N - 2, N - 1) * N % Mod + Mod) % Mod;
	for(int i = M + 1; i <= N && i <= 3 * M; i++)
		if((3 * M - i) % 2 == 0)
			ans = (ans - (1LL * C(N, i) * C((3 * M - i) / 2 + N - 1, N - 1) % Mod) + Mod) % Mod;
	printf("%d\n", ans);
	return 0;
}
```