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, deque, Counter
from heapq import heappush, heappop, heapify
import math
from bisect import bisect_left, bisect_right
import random
from itertools import permutations, accumulate, combinations
import sys
import string



INF = float('inf')
def LI(): return list(map(int, sys.stdin.readline().split()))
def I(): return int(sys.stdin.readline())
def LS(): return sys.stdin.readline().split()
def S(): return sys.stdin.readline().strip()
def IR(n): return [I() for i in range(n)]
def LIR(n): return [LI() for i in range(n)]
def SR(n): return [S() for i in range(n)]
def LSR(n): return [LS() for i in range(n)]
def SRL(n): return [list(S()) for i in range(n)]
def MSRL(n): return [[int(j) for j in list(S())] for i in range(n)]
mod = 998244353


n, m = LI()
total = m * 3

fac = [1] * (total+n+1)
inv = [1] * (total+n+1)
for i in range(total+n):
    fac[i+1] = fac[i]*(i+1)%mod

inv[total+n]=pow(fac[-1], mod-2, mod)
for j in range(total+n-1, -1, -1):
    inv[j]=inv[j+1]*(j+1)%mod



def comb(n, r):
    if r > n:
        return 0
    return fac[n] * inv[n - r] * inv[r] % mod


ans = comb(total+n-1, n-1)
for i in range(m + 2, min(n + 1, total + 1)):
    if (total - i) % 2 == 0:
        ans -= comb(n, i) * comb(n + (total - i) // 2 - 1, n - 1) % mod
        ans %= mod


ret = 0
for i in range(m):
    ret = (ret + comb(i + n - 2, n - 2)) % mod


ans -= (ret * n) % mod
print(ans % mod)