Buggy python submission (verdict: Runtime Error):
o,f,i=998244353,[1],1
while i<o/399:f+=f[-1]*i%o;i+=1
c=lambda n,k:f[n]*pow(f[n-k],o-2,o)*pow(f[k],o-2,o)
n,m=map(int,input().split())
w,u=3*m,n-1
a=c(w+u,u)-n*c(n+m-2,u)
if u>m:
 for i in range(m+1,min(w,n)+1):
  if w-i+1&1:a-=c(n,i)*c((w-i)//2+u,u) 
print(a%o)

Fixed submission:
mod = 998244353
rng = 2500100
fctr = [1]
finv = [1]
for i in range(1,rng):
  fctr.append(fctr[-1]*i%mod)
def inv(x):
  return pow(x,mod-2,mod)
def cmb(n,k):
  if n<0 or k<0:
    return 0
  else:
    return fctr[n]*inv(fctr[n-k])*inv(fctr[k])%mod

n,m = map(int,input().split())
ans = cmb(n+3*m-1,n-1)
ans = (ans-n*cmb(n+m-2,n-1))%mod
if n>m+1:
  for i in range(m+1,min(3*m,n)+1):
    if (3*m-i)%2 == 1:
      continue
    x = (3*m-i)//2
    ans = (ans-cmb(n,i)*cmb(x+n-1,n-1))%mod
print(ans)

Buggy python submission (verdict: Runtime Error):
o=998244353
f=[1]
for i in range(1,2500100):f.append(f[-1]*i%o)
c=lambda n,k: f[n]*pow(f[n-k],o-2,o)*pow(f[k],o-2,o)%o
n,m=map(int,input().split())
w=3*m
u=n-1
a=c(w+u,u)-n*c(n+m-2,u)
if u>m:
 for i in range(m+1,min(w,n)+1):
  a=(a-c(n,i)*c((w-i)//2+u,u))%o if w-i+1&1
print(a%o)

Fixed submission:
mod = 998244353
rng = 2500100
fctr = [1]
finv = [1]
for i in range(1,rng):
  fctr.append(fctr[-1]*i%mod)
def inv(x):
  return pow(x,mod-2,mod)
def cmb(n,k):
  if n<0 or k<0:
    return 0
  else:
    return fctr[n]*inv(fctr[n-k])*inv(fctr[k])%mod

n,m = map(int,input().split())
ans = cmb(n+3*m-1,n-1)
ans = (ans-n*cmb(n+m-2,n-1))%mod
if n>m+1:
  for i in range(m+1,min(3*m,n)+1):
    if (3*m-i)%2 == 1:
      continue
    x = (3*m-i)//2
    ans = (ans-cmb(n,i)*cmb(x+n-1,n-1))%mod
print(ans)

Buggy python submission (verdict: Runtime Error):
o=998244353
f=[1]
for i in range(1,2500100):f.append(f[-1]*i%o)
def c(n,k):return f[n]*pow(f[n-k],o-2,o)*pow(f[k],o-2,o)%o
n,m=map(int,input().split())
w=3*m
u=n-1
a=c(w+u,u)-n*c(n+m-2,u)
if u>m:
 for i in range(m+1,min(w,n)+1):
  if w-i+1&amp;1:a=(a-c(n,i)*c((w-i)//2+u,u))%o
print(a%o)

Fixed submission:
mod = 998244353
rng = 2500100
fctr = [1]
finv = [1]
for i in range(1,rng):
  fctr.append(fctr[-1]*i%mod)
def inv(x):
  return pow(x,mod-2,mod)
def cmb(n,k):
  if n<0 or k<0:
    return 0
  else:
    return fctr[n]*inv(fctr[n-k])*inv(fctr[k])%mod

n,m = map(int,input().split())
ans = cmb(n+3*m-1,n-1)
ans = (ans-n*cmb(n+m-2,n-1))%mod
if n>m+1:
  for i in range(m+1,min(3*m,n)+1):
    if (3*m-i)%2 == 1:
      continue
    x = (3*m-i)//2
    ans = (ans-cmb(n,i)*cmb(x+n-1,n-1))%mod
print(ans)

Buggy python submission (verdict: Runtime Error):
o=998244353
f=[1]
for i in range(1,2500100):f.append(f[-1]*i%o)
def c(n,k):return f[n]*pow(f[n-k],o-2,o)*pow(f[k],o-2,o)%o
n,m=map(int,input().split())
w=3*m
u=n-1
a=c(w+u,u)-n*c(n+m-2,u)
if u&gt;m:
 for i in range(m+1,min(w,n)+1):
  if w-i+1&amp;1:a=(a-c(n,i)*c((w-i)//2+u,u))%o
print(a%o)

Fixed submission:
mod = 998244353
rng = 2500100
fctr = [1]
finv = [1]
for i in range(1,rng):
  fctr.append(fctr[-1]*i%mod)
def inv(x):
  return pow(x,mod-2,mod)
def cmb(n,k):
  if n<0 or k<0:
    return 0
  else:
    return fctr[n]*inv(fctr[n-k])*inv(fctr[k])%mod

n,m = map(int,input().split())
ans = cmb(n+3*m-1,n-1)
ans = (ans-n*cmb(n+m-2,n-1))%mod
if n>m+1:
  for i in range(m+1,min(3*m,n)+1):
    if (3*m-i)%2 == 1:
      continue
    x = (3*m-i)//2
    ans = (ans-cmb(n,i)*cmb(x+n-1,n-1))%mod
print(ans)