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 PYTHON3):

Solution:
n,m=map(int,input().split())
w,u=3*m,n-1
o,f,i=998244353,[1],1
while i<w+n:f+=[f[-1]*i%o];i+=1
c=lambda n,k:f[n]*pow(f[n-k],o-2,o)*pow(f[k],o-2,o)
a=c(w+u,u)-n*c(n+m-2,u)
while n>-~m<w:m+=2;a-=c(n,m)*c(2*u+w-m>>1,u)
print(a%o)