Buggy python submission (verdict: Time Limit Exceeded):
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)
inv = [1] * (total + n)
i = 1
for j in range(1, total + n):
    i = i * j % mod
    fac[j] = i
    inv[j] = pow(i, mod - 2, 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)

Fixed submission:
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)

Buggy python submission (verdict: Time Limit Exceeded):
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)
inv = [1] * (total + n)
i = 1
for j in range(1, total + n):
    i = i * j % mod
    fac[j] = i
    inv[j] = pow(i, mod - 2, 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), 2):
    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)

Fixed submission:
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)

Buggy python submission (verdict: Time Limit Exceeded):
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)
inv = [1] * (total + n)
i = 1
for j in range(1, total + n):
    i = i * j % mod
    fac[j] = i
    inv[j] = pow(i, mod - 2, mod)



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



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


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


impossible = (impossible + ret * n) % mod


ret = 0
print((comb(total + n - 1, n - 1) - impossible) % mod)

Fixed submission:
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)