Buggy python submission (verdict: Runtime Error):
p=10**9+7
X, Y=map(int, input().split())

if (X+Y)%3>0:
  print(0)
  exit()
  
a=(2*X-Y)//3
b=(2*Y-X)//3

ab=a+b
ue=[1]*(ab+1)
for i in range(1, ab+1):
  ue[i]=ue[i-1]*i%p
  
out=ue[-1]*pow(ue[a], p-2, p)%p
out=out*pow(ue[b], p-2, p)%p

print(out)

Fixed submission:
p=10**9+7
X, Y=map(int, input().split())

if (X+Y)%3>0:
  print(0)
  exit()
  
a=(2*X-Y)//3
b=(2*Y-X)//3

if a*b<0:
  print(0)
  exit()

ab=a+b
ue=[1]*(ab+1)
for i in range(1, ab+1):
  ue[i]=ue[i-1]*i%p
  
out=ue[-1]*pow(ue[a], p-2, p)%p
out=out*pow(ue[b], p-2, p)%p

print(out)

Buggy python submission (verdict: Runtime Error):
def extgcd(a,b):
    r = [1,0,a]
    w = [0,1,b]
    while w[2]!=1:
        q = r[2]//w[2]
        r2 = w
        w2 = [r[0]-q*w[0],r[1]-q*w[1],r[2]-q*w[2]]
        r = r2
        w = w2
    return [w[0],w[1]]

def mod_inv(a,m):
    x = extgcd(a,m)[0]
    return (m+x%m)%m

X, Y=map(int, input().split())
 
def f(x, y):
  s=max(x, y)
  t=min(x, y)
  st=s+t
  ans=1
  for i in range(1, t+1):
    ans=ans*(st+1-i)//i
    ans=ans%(10**9+6)
    
  return ans
  
      
b=(2*X-Y)//3
btemp=(2*X-Y)%3
a=(Y-a)//2
atemp=(Y-a)%2
if btemp>0 or atemp>0:
  ans=0
else:
  a=(Y-b)//2
  
  #ans=mt.factorial(a+b)//(mt.factorial(a)*mt.factorial(b))
  #ans=tool.permutations(a+b)//(tool.permutations(a)*tool.permutations(b))
  #s=max(a, b)
  #t=min(a, b)
  #ans=comb(s+t, t, 10**9+7)
  m=10**9+7
  ans=1
  for i in range(1, a+b+1):
    ans=ans*i%m
  for i in range(1, a+1):
    ans=ans*mod_inv(i, m)%m
  for i in range(1, b+1):
    ans=ans*mod_inv(i, m)%m
print(ans)


Fixed submission:
p=10**9+7
X, Y=map(int, input().split())

if (X+Y)%3>0:
  print(0)
  exit()
  
a=(2*X-Y)//3
b=(2*Y-X)//3

if a*b<0:
  print(0)
  exit()

ab=a+b
ue=[1]*(ab+1)
for i in range(1, ab+1):
  ue[i]=ue[i-1]*i%p
  
out=ue[-1]*pow(ue[a], p-2, p)%p
out=out*pow(ue[b], p-2, p)%p

print(out)

Buggy python submission (verdict: Time Limit Exceeded):
from math import factorial
 
def comb(n,k,p):
  if n<0 or k<0 or n<k: return 0
  if n==0 or k==0: return 1
  a=factorial(n) %p
  b=factorial(k) %p
  c=factorial(n-k) %p
  return (a*power_func(b,p-2,p)*power_func(c,p-2,p))%p
def power_func(a,b,p):
  if b==0: return 1
  if b%2==0:
    d=power_func(a,b//2,p)
    return d*d %p
  if b%2==1:
    return (a*power_func(a,b-1,p ))%p
 
X, Y=map(int, input().split())
 
def f(x, y):
  s=max(x, y)
  t=min(x, y)
  st=s+t
  ans=1
  for i in range(1, t+1):
    ans=ans*(st+1-i)//i
    ans=ans%(10**9+6)
    
  return ans
  
      
b=(2*X-Y)//3
btemp=(2*X-Y)%3
if btemp>0:
  ans=0
else:
  a=(Y-b)//2
  
  #ans=mt.factorial(a+b)//(mt.factorial(a)*mt.factorial(b))
  #ans=tool.permutations(a+b)//(tool.permutations(a)*tool.permutations(b))
  s=max(a, b)
  t=min(a, b)
  ans=comb(s+t, t, 10**9+7)
print(ans)

Fixed submission:
p=10**9+7
X, Y=map(int, input().split())

if (X+Y)%3>0:
  print(0)
  exit()
  
a=(2*X-Y)//3
b=(2*Y-X)//3

if a*b<0:
  print(0)
  exit()

ab=a+b
ue=[1]*(ab+1)
for i in range(1, ab+1):
  ue[i]=ue[i-1]*i%p
  
out=ue[-1]*pow(ue[a], p-2, p)%p
out=out*pow(ue[b], p-2, p)%p

print(out)

Buggy python submission (verdict: Time Limit Exceeded):
from math import factorial

def comb(n,k,p):
  if n<0 or k<0 or n<k: return 0
  if n==0 or k==0: return 1
  a=factorial(n) %p
  b=factorial(k) %p
  c=factorial(n-k) %p
  return (a*power_func(b,p-2,p)*power_func(c,p-2,p))%p
def power_func(a,b,p):
  if b==0: return 1
  if b%2==0:
    d=power_func(a,b//2,p)
    return d*d %p
  if b%2==1:
    return (a*power_func(a,b-1,p ))%p

X, Y=map(int, input().split())

def f(x, y):
  s=max(x, y)
  t=min(x, y)
  st=s+t
  ans=1
  for i in range(1, t+1):
    ans=ans*(st+1-i)//i
    ans=ans%(10**9+6)
    
  return ans
  
      
b=(2*X-Y)//3
btemp=(2*X-Y)%3
if btemp>0:
  ans=0
else:
  a=(Y-b)//2
  
  #ans=mt.factorial(a+b)//(mt.factorial(a)*mt.factorial(b))
  #ans=tool.permutations(a+b)//(tool.permutations(a)*tool.permutations(b))
  s=max(a, b)
  t=min(a, b)
  ans=comb(s+t, t, 10**9+7)
print(ans)

Fixed submission:
p=10**9+7
X, Y=map(int, input().split())

if (X+Y)%3>0:
  print(0)
  exit()
  
a=(2*X-Y)//3
b=(2*Y-X)//3

if a*b<0:
  print(0)
  exit()

ab=a+b
ue=[1]*(ab+1)
for i in range(1, ab+1):
  ue[i]=ue[i-1]*i%p
  
out=ue[-1]*pow(ue[a], p-2, p)%p
out=out*pow(ue[b], p-2, p)%p

print(out)