Buggy python submission (verdict: Runtime Error):
a,b = map(int,input().split())
if (a+b)%3 == 0:
  n = (a+b)/3
  import math
  aa = math.factorial(a-n)
  bb = math.factorial(b-n)
  cc = math.factorial(n)
  print((cc/(bb*aa))%(10**9+7))
else:
  print(0)

Fixed submission:
import math
import numpy as np

def cmb(n, r, mod):
  r = min(r, n-r)
  return g1[n] * g2[r] * g2[n-r] % mod

mod = 10**9+7 
N = 10**6
g1 = [1, 1] 
g2 = [1, 1] 
inverse = [0, 1] 

for i in range( 2, N + 1 ):
  g1.append( ( g1[-1] * i ) % mod )
  inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
  g2.append( (g2[-1] * inverse[-1]) % mod )

x,y = map(int,input().split()) 

if (x+y) % 3 == 0:

  A = np.array([[1, 2],
                [2, 1]])

  b = np.array([x, y])

  N = np.linalg.solve(A, b)


  if N[0].is_integer() == True and N[1].is_integer() == True and N[0] >=0 and N[1] >=0:
        
      print(cmb(int(N[0]+N[1]),int(N[0]),mod))

  else:
      print(0)

else:
  print(0)

Buggy python submission (verdict: Runtime Error):
a,b = map(int,input().split())
if (a+b)%3 == 0:
  n = (a+b)/3
  aa = math.factorial(a-n)
  bb = math.factorial(b-n)
  cc = math.factorial(n)
  print((cc/(bb*aa))%(10**9+7))
else:
  print(0)

Fixed submission:
import math
import numpy as np

def cmb(n, r, mod):
  r = min(r, n-r)
  return g1[n] * g2[r] * g2[n-r] % mod

mod = 10**9+7 
N = 10**6
g1 = [1, 1] 
g2 = [1, 1] 
inverse = [0, 1] 

for i in range( 2, N + 1 ):
  g1.append( ( g1[-1] * i ) % mod )
  inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
  g2.append( (g2[-1] * inverse[-1]) % mod )

x,y = map(int,input().split()) 

if (x+y) % 3 == 0:

  A = np.array([[1, 2],
                [2, 1]])

  b = np.array([x, y])

  N = np.linalg.solve(A, b)


  if N[0].is_integer() == True and N[1].is_integer() == True and N[0] >=0 and N[1] >=0:
        
      print(cmb(int(N[0]+N[1]),int(N[0]),mod))

  else:
      print(0)

else:
  print(0)

Buggy python submission (verdict: Runtime Error):
a,b = map(int,input().split())
if (a+b)%3 == 0:
  a == a - min(a,b)
  b == b - min(a,b)
  c = a+b
  import math
  aa = math.factorial(a)
  bb = math.factorial(b)
  cc = math.factorial(c)
  print((cc/(bb*aa))%(10**9+7))
else:
  print(0)

Fixed submission:
import math
import numpy as np

def cmb(n, r, mod):
  r = min(r, n-r)
  return g1[n] * g2[r] * g2[n-r] % mod

mod = 10**9+7 
N = 10**6
g1 = [1, 1] 
g2 = [1, 1] 
inverse = [0, 1] 

for i in range( 2, N + 1 ):
  g1.append( ( g1[-1] * i ) % mod )
  inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
  g2.append( (g2[-1] * inverse[-1]) % mod )

x,y = map(int,input().split()) 

if (x+y) % 3 == 0:

  A = np.array([[1, 2],
                [2, 1]])

  b = np.array([x, y])

  N = np.linalg.solve(A, b)


  if N[0].is_integer() == True and N[1].is_integer() == True and N[0] >=0 and N[1] >=0:
        
      print(cmb(int(N[0]+N[1]),int(N[0]),mod))

  else:
      print(0)

else:
  print(0)

Buggy python submission (verdict: Time Limit Exceeded):
import math
import numpy as np

x,y = map(int,input().split()) 

A = np.array([[1, 2],
           [2, 1]])

b = np.array([x, y])

N = np.linalg.solve(A, b)


if N[0].is_integer() == True and N[1].is_integer() == True and N[0] >=0 and N[1] >=0:
  
  k = math.factorial(N[0]+N[1])/(math.factorial(N[0])*math.factorial(N[1]))

  print(int(k%1000000007))

else:
  print(0)


Fixed submission:
import math
import numpy as np

def cmb(n, r, mod):
  r = min(r, n-r)
  return g1[n] * g2[r] * g2[n-r] % mod

mod = 10**9+7 
N = 10**6
g1 = [1, 1] 
g2 = [1, 1] 
inverse = [0, 1] 

for i in range( 2, N + 1 ):
  g1.append( ( g1[-1] * i ) % mod )
  inverse.append( ( -inverse[mod % i] * (mod//i) ) % mod )
  g2.append( (g2[-1] * inverse[-1]) % mod )

x,y = map(int,input().split()) 

if (x+y) % 3 == 0:

  A = np.array([[1, 2],
                [2, 1]])

  b = np.array([x, y])

  N = np.linalg.solve(A, b)


  if N[0].is_integer() == True and N[1].is_integer() == True and N[0] >=0 and N[1] >=0:
        
      print(cmb(int(N[0]+N[1]),int(N[0]),mod))

  else:
      print(0)

else:
  print(0)