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:
import sys
input=sys.stdin.readline
N,M=map(int,input().split())
mod=998244353

inv=[0]*(3*M//2+N+2)
inv[1]=1
for i in range(2,3*M//2+N+2):
    inv[i]=-(mod//i)*inv[mod%i]%mod

#階乗テーブル
g1=[1,1]
g2=[1,1]
for i in range(2,3*M//2+N+2):
    num_1=g1[-1]*i%mod
    g1.append(num_1)
    g2.append(g2[-1]*inv[i]%mod)
    
def cmb(n,r):
    return g1[n]*g2[r]*g2[n-r]%mod

#奇数の和で場合分け
#iは奇数の数

ans=0
for i in range(min(N+1,M+1)):
    if M%2!=i%2:
        continue
    m=(3*M-i)//2
    num=(cmb(m+N-1,N-1)-i*cmb(m-M+N-1,N-1))%mod
    if m>=M+1:
        num=(num-(N-i)*cmb(m-M+N-2,N-1))%mod
    ans=(ans+cmb(N,i)*num)%mod

print(ans)