Problem Statement

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.

Sample Input 1

2 2

Sample Output 1

3

After two operations, there are three possible outcomes:

• x=(2,4)
• x=(3,3)
• x=(4,2)

For example, x=(3,3) can result after the following sequence of operations:

• First, choose i=0,j=1, changing x from (0,0) to (2,1).
• Second, choose i=1,j=0, changing x from (2,1) to (3,3).

Sample Input 2

3 2

Sample Output 2

19

Sample Input 3

10 10

Sample Output 3

211428932

Sample Input 4

100000 50000

Sample Output 4

3463133