Buggy python submission (verdict: Runtime Error):
def cmb(n, r, p):
    if (r < 0) or (n < r):
        return 0
    r = min(r, n - r)
    return fact[n] * factinv[r] * factinv[n-r] % p

p = 10**9 + 7
N = 10**6  # N は必要分だけ用意する
fact = [1, 1]  # fact[n] = (n! mod p)
factinv = [1, 1]  # factinv[n] = ((n!)^(-1) mod p)
inv = [0, 1]  # factinv 計算用
 
for i in range(2, N+1):
    fact.append((fact[-1] * i) % p)
    inv.append((-inv[p % i] * (p // i)) % p)
    factinv.append((factinv[-1] * inv[-1]) % p)

x,y=map(int,input().split())
ans=0
x_3=x//3
y_3=y//3
kyo2=min(x_3,y_3)
xx=x-kyo2*3
yy=y-kyo2*3

#print(xx,yy,kyo2)
    
if (xx==0 and yy==0):
  ans=cmb(2*kyo2,kyo2,p)
  print(ans)
elif (xx/yy==2):
  ans=cmb(2*kyo2+yy,kyo2,p)
  print(ans)
elif (yy/xx==2):
  ans=cmb(2*kyo2+xx,kyo2,p)
  print(ans)
else:
  print(0)
  

Fixed submission:
def cmb(n, r, p):
    if (r < 0) or (n < r):
        return 0
    r = min(r, n - r)
    return fact[n] * factinv[r] * factinv[n-r] % p

p = 10**9 + 7
N = 10**6  # N は必要分だけ用意する
fact = [1, 1]  # fact[n] = (n! mod p)
factinv = [1, 1]  # factinv[n] = ((n!)^(-1) mod p)
inv = [0, 1]  # factinv 計算用
 
for i in range(2, N+1):
    fact.append((fact[-1] * i) % p)
    inv.append((-inv[p % i] * (p // i)) % p)
    factinv.append((factinv[-1] * inv[-1]) % p)

    
x,y=map(int,input().split())
if ((x+y)%3!=0):
  print(0)
else:
  xx=(2*x-y)//3
  yy=(2*y-x)//3
  if (xx<0 or yy<0):
    print(0)
  else:
    ans=cmb(xx+yy,xx,p)
    print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
def cmb(n, r, p):
    if (r < 0) or (n < r):
        return 0
    r = min(r, n - r)
    return fact[n] * factinv[r] * factinv[n-r] % p

p = 10**9 + 7
N = 10**7  # N は必要分だけ用意する
fact = [1, 1]  # fact[n] = (n! mod p)
factinv = [1, 1]  # factinv[n] = ((n!)^(-1) mod p)
inv = [0, 1]  # factinv 計算用
 
for i in range(2, N+1):
    fact.append((fact[-1] * i) % p)
    inv.append((-inv[p % i] * (p // i)) % p)
    factinv.append((factinv[-1] * inv[-1]) % p)

x,y=map(int,input().split())
ans=0
x_3=x//3
y_3=y//3
kyo2=min(x_3,y_3)
xx=x-kyo2*3
yy=y-kyo2*3

#print(xx,yy,kyo2)
    
if (xx==0 and yy==0):
  ans=cmb(2*kyo2,kyo2,p)
  print(ans)
elif (xx/yy==2):
  ans=cmb(2*kyo2+yy,kyo2,p)
  print(ans)
elif (yy/xx==2):
  ans=cmb(2*kyo2+xx,kyo2,p)
  print(ans)
else:
  print(0)
  

Fixed submission:
def cmb(n, r, p):
    if (r < 0) or (n < r):
        return 0
    r = min(r, n - r)
    return fact[n] * factinv[r] * factinv[n-r] % p

p = 10**9 + 7
N = 10**6  # N は必要分だけ用意する
fact = [1, 1]  # fact[n] = (n! mod p)
factinv = [1, 1]  # factinv[n] = ((n!)^(-1) mod p)
inv = [0, 1]  # factinv 計算用
 
for i in range(2, N+1):
    fact.append((fact[-1] * i) % p)
    inv.append((-inv[p % i] * (p // i)) % p)
    factinv.append((factinv[-1] * inv[-1]) % p)

    
x,y=map(int,input().split())
if ((x+y)%3!=0):
  print(0)
else:
  xx=(2*x-y)//3
  yy=(2*y-x)//3
  if (xx<0 or yy<0):
    print(0)
  else:
    ans=cmb(xx+yy,xx,p)
    print(ans)

Buggy python submission (verdict: Runtime Error):
def cmb(n, r, p):
    if (r < 0) or (n < r):
        return 0
    r = min(r, n - r)
    return fact[n] * factinv[r] * factinv[n-r] % p

p = 10 ** 9 + 7
N = 10 ** 6  # N は必要分だけ用意する
fact = [1, 1]  # fact[n] = (n! mod p)
factinv = [1, 1]  # factinv[n] = ((n!)^(-1) mod p)
inv = [0, 1]  # factinv 計算用
 
for i in range(2, N + 1):
    fact.append((fact[-1] * i) % p)
    inv.append((-inv[p % i] * (p // i)) % p)
    factinv.append((factinv[-1] * inv[-1]) % p)

x,y=map(int,input().split())
ans=0
x_3=x//3
y_3=y//3
kyo2=min(x_3,y_3)
xx=x-kyo2*3
yy=y-kyo2*3

#print(xx,yy,kyo2)
    
if (xx==0 and yy==0):
  ans=cmb(2*kyo2,kyo2,p)
  print(ans)
elif (xx/yy==2):
  ans=cmb(2*kyo2+yy,kyo2,p)
  print(ans)
elif (yy/xx==2):
  ans=cmb(2*kyo2+xx,kyo2,p)
  print(ans)
else:
  print(0)
  

Fixed submission:
def cmb(n, r, p):
    if (r < 0) or (n < r):
        return 0
    r = min(r, n - r)
    return fact[n] * factinv[r] * factinv[n-r] % p

p = 10**9 + 7
N = 10**6  # N は必要分だけ用意する
fact = [1, 1]  # fact[n] = (n! mod p)
factinv = [1, 1]  # factinv[n] = ((n!)^(-1) mod p)
inv = [0, 1]  # factinv 計算用
 
for i in range(2, N+1):
    fact.append((fact[-1] * i) % p)
    inv.append((-inv[p % i] * (p // i)) % p)
    factinv.append((factinv[-1] * inv[-1]) % p)

    
x,y=map(int,input().split())
if ((x+y)%3!=0):
  print(0)
else:
  xx=(2*x-y)//3
  yy=(2*y-x)//3
  if (xx<0 or yy<0):
    print(0)
  else:
    ans=cmb(xx+yy,xx,p)
    print(ans)