Buggy python submission (verdict: Runtime Error):
import math
X,Y = map(int,input().split())
a,b = (2*Y-X)/3,(2*X-Y)/3
n = 10**9+7
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

mod = 10**9+7 #出力の制限
N = 10**4
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 )
def count():
  if not (a//1 == a and b//1==b):
    return 0
  else:
    ahat = int(a%n)
    bhat = int(b%n)
    return cmb(ahat+bhat,ahat)


print(int(count())%(10**9+7))

Fixed submission:
import math
X,Y = map(int,input().split())
a,b = (2*Y-X)/3,(2*X-Y)/3
n = 10**9+7
def cmb(n, r, mod=10**9+7):
    n1, r = n+1, min(r, n-r)
    numer = denom = 1
    for i in range(1, r+1):
        numer = numer * (n1-i) % mod
        denom = denom * i % mod
    return numer * pow(denom, mod-2, mod) % mod
def count():
  if not (a//1 == a and b//1==b):
    return 0
  else:
    ahat = int(a%n)
    bhat = int(b%n)
    return cmb(ahat+bhat,ahat)


print(int(count())%(10**9+7))

Buggy python submission (verdict: Time Limit Exceeded):
import math
X,Y = map(int,input().split())
a,b = (2*Y-X)/3,(2*X-Y)/3
n = 10**9+7
nCr={}
def cmb(n, r):
    if n - r < r: r = n - r
    if r == 0: return 1
    if r == 1: return n

    numerator = [n - r + k + 1 for k in range(r)]
    denominator = [k + 1 for k in range(r)]

    for p in range(2,r+1):
        pivot = denominator[p - 1]
        if pivot > 1:
            offset = (n - r) % p
            for k in range(p-1,r,p):
                numerator[k - offset] /= pivot
                denominator[k] /= pivot

    result = 1
    for k in range(r):
        if numerator[k] > 1:
            result *= int(numerator[k])

    return result
def count():
  if not (a//1 == a and b//1==b):
    return 0
  else:
    ahat = int(a%n)
    bhat = int(b%n)
    return cmb(ahat+bhat,ahat)


print(int(count())%(10**9+7))

Fixed submission:
import math
X,Y = map(int,input().split())
a,b = (2*Y-X)/3,(2*X-Y)/3
n = 10**9+7
def cmb(n, r, mod=10**9+7):
    n1, r = n+1, min(r, n-r)
    numer = denom = 1
    for i in range(1, r+1):
        numer = numer * (n1-i) % mod
        denom = denom * i % mod
    return numer * pow(denom, mod-2, mod) % mod
def count():
  if not (a//1 == a and b//1==b):
    return 0
  else:
    ahat = int(a%n)
    bhat = int(b%n)
    return cmb(ahat+bhat,ahat)


print(int(count())%(10**9+7))

Buggy python submission (verdict: Time Limit Exceeded):
import math
X,Y = map(int,input().split())
a,b = (2*Y-X)/3,(2*X-Y)/3
n = 10**9+7
nCr={}
def cmb(n, r):
    if n - r < r: r = n - r
    if r == 0: return 1
    if r == 1: return n

    numerator = [n - r + k + 1 for k in range(r)]
    denominator = [k + 1 for k in range(r)]

    for p in range(2,r+1):
        pivot = denominator[p - 1]
        if pivot > 1:
            offset = (n - r) % p
            for k in range(p-1,r,p):
                numerator[k - offset] /= pivot
                denominator[k] /= pivot

    result = 1
    for k in range(r):
        if numerator[k] > 1:
            result *= int(numerator[k])

    return result
def count():
  if not (a//1 == a and b//1==b):
    return 0
  else:
    ahat = int(a%n)
    bhat = int(b%n)
    return cmb(ahat+bhat,ahat)


print(int(count())%(10**9+7))

Fixed submission:
import math
X,Y = map(int,input().split())
a,b = (2*Y-X)/3,(2*X-Y)/3
n = 10**9+7
def cmb(n, r, mod=10**9+7):
    n1, r = n+1, min(r, n-r)
    numer = denom = 1
    for i in range(1, r+1):
        numer = numer * (n1-i) % mod
        denom = denom * i % mod
    return numer * pow(denom, mod-2, mod) % mod
def count():
  if not (a//1 == a and b//1==b):
    return 0
  else:
    ahat = int(a%n)
    bhat = int(b%n)
    return cmb(ahat+bhat,ahat)


print(int(count())%(10**9+7))

Buggy python submission (verdict: Time Limit Exceeded):
import math
X,Y = map(int,input().split())
a,b = (2*Y-X)/3,(2*X-Y)/3
n = 10**9+7
nCr={}
def cmb(n, r):
    if n - r < r: r = n - r
    if r == 0: return 1
    if r == 1: return n

    numerator = [n - r + k + 1 for k in range(r)]
    denominator = [k + 1 for k in range(r)]

    for p in range(2,r+1):
        pivot = denominator[p - 1]
        if pivot > 1:
            offset = (n - r) % p
            for k in range(p-1,r,p):
                numerator[k - offset] /= pivot
                denominator[k] /= pivot

    result = 1
    for k in range(r):
        if numerator[k] > 1:
            result *= int(numerator[k])

    return result
def count():
  if not (a//1 == a and b//1==b):
    return 0
  else:
    ahat = int(a%n)
    bhat = int(b%n)
    return cmb(ahat+bhat,ahat)


print(int(count())%(10**9+7))

Fixed submission:
import math
X,Y = map(int,input().split())
a,b = (2*Y-X)/3,(2*X-Y)/3
n = 10**9+7
def cmb(n, r, mod=10**9+7):
    n1, r = n+1, min(r, n-r)
    numer = denom = 1
    for i in range(1, r+1):
        numer = numer * (n1-i) % mod
        denom = denom * i % mod
    return numer * pow(denom, mod-2, mod) % mod
def count():
  if not (a//1 == a and b//1==b):
    return 0
  else:
    ahat = int(a%n)
    bhat = int(b%n)
    return cmb(ahat+bhat,ahat)


print(int(count())%(10**9+7))