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 JAVA):

Solution:
import java.util.*;
public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		prepareFact();
		int n = sc.nextInt();
		int m = sc.nextInt();
		int sum = m * 3;
		long ans = combiMod(n - 1 + sum, n - 1);
		for(int i = m * 2 + 1; i <= sum; i ++) {
			long tmp = combiMod(n - 2 + (sum - i), n - 2);
			tmp = mod(tmp * (long)n);
			ans = mod(ans - tmp);
		}

		long minus = 0;
		for(int i = m + 2; i <= n; i += 2) {
			long tmp = permMod(n - 1 + (sum - i) / 2, n - 1);
			tmp = mod(tmp * combiMod(n, i));
			minus = mod(minus + tmp);
		}
		minus = mod(minus * invMod(factMod[n - 1]));
		ans = mod(ans - minus);
		System.out.println(ans);
	}

	static long MOD = 998244353;
	public static long mod(long i) {
		return i % MOD + ((i % MOD) < 0 ? MOD : 0);
	}
	
	static long powerMod(long x, long y) {
		if (y == 0) {
			return 1;
		} else if (y == 1) {
			return x;
		} else if (y % 2 == 0) {
			long tmp = powerMod(x, y / 2);
			return mod(tmp * tmp);
		} else {
			long tmp = powerMod(x, y / 2);
			return mod(mod(tmp * tmp) * x);
		}
	}
	
	static long invMod(long x) {
		return powerMod(x, MOD - 2);
	}
	
	static int MAX_FACT = 2_500_100;
	static long factMod[] = new long[MAX_FACT];
	static void prepareFact() {
		factMod[0] = 1;
		for(int i = 1; i < MAX_FACT; i ++) {
			factMod[i] = mod(factMod[i - 1] * i);
		}
	}
	
	static long combiMod(int n, int r) {
		if(n < 0 || n < r) { return 0; }
		if(r == 0 || r == n) { return 1; }
		return mod(mod(factMod[n] * invMod(factMod[r])) * invMod(factMod[n - r]));
	}

	static long permMod(int n, int r) {
		if(n < 0 || n < r) { return 0; }
		if(r == 0) { return 1; }
		return mod(factMod[n] * invMod(factMod[n - r]));
	}
}