Buggy python submission (verdict: Runtime Error):
import sys
import math
x,y=map(int,input().split())
if (x+y)%3!=0:
  print(0)
  sys.exit()
n=(x+y)//3
print(math.factorial(n)//math.factorial(x-n)//math.factorial(y-n))

Fixed submission:
import sys
def cmb(n, r, mod):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod

x,y=map(int,input().split())
if (x+y)%3!=0:
  print(0)
  sys.exit()
n=(x+y)//3

mod = 10**9+7 #出力の制限
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル

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 )

print(cmb(n,x-n,mod))

Buggy python submission (verdict: Runtime Error):
import sys
import math
x,y=map(int,input().split())
if (x+y)%3!=0:
  print(0)
  sys.exit()
n=(x+y)//3
print(math_factorial(n)//math_factorial(x-n)//math_factorial(y-n))

Fixed submission:
import sys
def cmb(n, r, mod):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod

x,y=map(int,input().split())
if (x+y)%3!=0:
  print(0)
  sys.exit()
n=(x+y)//3

mod = 10**9+7 #出力の制限
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル

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 )

print(cmb(n,x-n,mod))

Buggy python submission (verdict: Time Limit Exceeded):
import sys
x,y=map(int,input().split())
if (x+y)%3!=0:
  print(0)
  sys.exit()
n=(x+y)//3
fac=[1 for i in range(n+1)]#fac[i]=i!. fac[0]=1
for i in range(1,n+1):
  fac[i]=fac[i-1]*i

print(fac[n]//fac[x-n]//fac[y-n])

Fixed submission:
import sys
def cmb(n, r, mod):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod

x,y=map(int,input().split())
if (x+y)%3!=0:
  print(0)
  sys.exit()
n=(x+y)//3

mod = 10**9+7 #出力の制限
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル

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 )

print(cmb(n,x-n,mod))

Buggy python submission (verdict: Runtime Error):
import sys
x,y=map(int,input().split())
if (x+y)%3!=0:
  print(0)
  sys.exit()
n=(x+y)//3
fac=[1 for i in range(n+1)]#fac[i]=i!. fac[0]=1
for i in range(n+1):
  fac[i]=fac[i-1]*i

print(fac[n]//fac[x-n]//fac[y-n])

Fixed submission:
import sys
def cmb(n, r, mod):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod

x,y=map(int,input().split())
if (x+y)%3!=0:
  print(0)
  sys.exit()
n=(x+y)//3

mod = 10**9+7 #出力の制限
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル

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 )

print(cmb(n,x-n,mod))

Buggy python submission (verdict: Runtime Error):
inport sys
x,y=map(int,input().split())
if (x+y)%3!=0:
  print(0)
  sys.exit()
n=(x+y)//3
fac=[1 for i in range(n+1)]#fac[i]=i!. fac[0]=1
for i in range(n+1):
  fac[i]=fac[i-1]*i

print(fac[n]//fac[x-n]//fac[y-n])

Fixed submission:
import sys
def cmb(n, r, mod):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod

x,y=map(int,input().split())
if (x+y)%3!=0:
  print(0)
  sys.exit()
n=(x+y)//3

mod = 10**9+7 #出力の制限
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル

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 )

print(cmb(n,x-n,mod))

Buggy python submission (verdict: Runtime Error):
inport sys
fac=[1 for i in range(n+1)]#fac[i]=i!. fac[0]=1
for i in range(n+1):
  fac[i]=fac[i-1]*i

def comb(n,k):
  return fac[n]//fac[k]//fac[n-k]

x,y=map(int,input().split())
if (x+y)%3!=0:
  print(0)
  sys.exit()
n=(x+y)//3
print(comb(n,x-n))

Fixed submission:
import sys
def cmb(n, r, mod):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod

x,y=map(int,input().split())
if (x+y)%3!=0:
  print(0)
  sys.exit()
n=(x+y)//3

mod = 10**9+7 #出力の制限
g1 = [1, 1] # 元テーブル
g2 = [1, 1] #逆元テーブル
inverse = [0, 1] #逆元テーブル計算用テーブル

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 )

print(cmb(n,x-n,mod))