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

Difficulty: UNKNOWN_DIFFICULTY

Solutions:
(N, M) = map(int, input().split())
MOD = 998244353
if N < M:
	one = N - (N - M) % 2
	two = (3 * M - one) // 2
else:
	(one, two) = (M, M)
L = M + M // 2 + N - 1
fac = [0] * (L + 1)
inv = [0] * (L + 1)
(fac[0], inv[0]) = (1, 1)
for i in range(1, L + 1):
	fac[i] = fac[i - 1] * i % MOD
	inv[i] = pow(fac[i], MOD - 2, MOD)

def comb(n, r):
	if n <= 0 or r < 0:
		return 0
	return fac[n] * inv[n - r] * inv[r] % MOD
ret = 0
while one >= 0:
	ret += comb(N, one) * comb(two + N - 1, N - 1) % MOD
	ret %= MOD
	one -= 2
	two += 1
ret -= comb(3 * M + N - 1 - (2 * M + 1), N - 1) * N
print(ret % MOD)


from collections import defaultdict, deque, Counter
from heapq import heappush, heappop, heapify
import math
import bisect
import random
from itertools import permutations, accumulate, combinations, product
import sys
from pprint import pprint
from copy import deepcopy
import string
from bisect import bisect_left, bisect_right
from math import factorial, ceil, floor
from operator import mul
from functools import reduce
from pprint import pprint
sys.setrecursionlimit(2147483647)
INF = 10 ** 15

def LI():
	return list(map(int, sys.stdin.buffer.readline().split()))

def I():
	return int(sys.stdin.buffer.readline())

def LS():
	return sys.stdin.buffer.readline().rstrip().decode('utf-8').split()

def S():
	return sys.stdin.buffer.readline().rstrip().decode('utf-8')

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()
a = n + 3 * m
fac = [1] * (a + 1)
inv = [1] * (a + 1)
for j in range(1, a + 1):
	fac[j] = fac[j - 1] * j % mod
inv[a] = pow(fac[a], mod - 2, mod)
for j in range(a - 1, -1, -1):
	inv[j] = inv[j + 1] * (j + 1) % mod

def comb(x, y):
	if y > x or x < 0 or y < 0:
		return 0
	return fac[x] * inv[x - y] * inv[y] % mod
ans = 0
for i in range(min(m + 1, n + 1)):
	if (m - i) % 2:
		continue
	ans += comb(n, i) * comb((m * 3 - i) // 2 + n - 1, n - 1)
	ans %= mod
print((ans - n * comb(m - 1 + n - 1, n - 1)) % mod)


class comb:
	F = [1, 1]
	Fi = [1, 1]
	I = [0, 1]

	def __init__(self, num, mod):
		self.MOD = mod
		for i in range(2, num + 1):
			self.F.append(self.F[-1] * i % mod)
			self.I.append(mod - self.I[mod % i] * (mod // i) % mod)
			self.Fi.append(self.Fi[-1] * self.I[i] % mod)

	def com(self, n, k):
		if n < k:
			return 0
		if n < 0 or k < 0:
			return 0
		return self.F[n] * (self.Fi[k] * self.Fi[n - k] % self.MOD) % self.MOD
(N, M) = list(map(int, input().split()))
MOD = 998244353
com = comb(M * 3 + N, MOD)
t = com.com(M * 3 + N - 1, N - 1)
t -= com.com(M - 1 + N - 1, N - 1) * N
while t < 0:
	t += MOD
if N > M:
	for k in range(M + 2, N + 1, 2):
		i = (M * 3 - k) // 2
		t -= com.com(N, k) * com.com(N - 1 + i, i) % MOD
	while t < 0:
		t += MOD
print(t)


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):
		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):
		fact_inv = [1] * (n + 1)
		fact_inv[n] = pow(self.fact[n], self.mod - 2, self.mod)
		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)