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:
from collections import defaultdict
class Combination():
    def __init__(self, n, mod):
        self.n = n
        self.mod = mod
        self.fact = self.make_fact(n)
        self.fact_inv = self.make_fact_inv(n)
    def make_fact(self, n):#0~nの階乗を求める
        res = [1]*(n+1)
        for i in range(1, n+1):
            res[i] = res[i-1]*i%self.mod
        return res
    def make_fact_inv(self, n):#0~nの階乗のmodに関する逆元を求める
        fact_inv = [1]*(n+1)
        fact_inv[n] = pow(self.fact[n], self.mod-2, self.mod)#フェルマーの小定理
        for i in range(n, 0, -1):
            fact_inv[i-1] = fact_inv[i]*i%self.mod
        return fact_inv
    def comb(self, m, k):
        if m<0 or k<0 or m<k:
            return 0
        return self.fact[m]*self.fact_inv[k]*self.fact_inv[m-k]%self.mod
mod = 998244353
n, m = map(int, input().split())
C = Combination(n+m*3, mod)
ans = 0
for i in range(min(n, m)+1):
    if m%2 != i%2:
        continue
    res = 0
    r = (m*3-i)//2
    res+=C.comb(r+n-1, r)
    res-=C.comb(r-m-1+n-1, n-1)*(n-i)
    res-=C.comb(r-m+n-1, n-1)*i
    res*=C.comb(n, i)
    res%-mod
    ans+=res
    ans%=mod
print(ans)