Buggy python submission (verdict: Time Limit Exceeded):
from scipy.misc import comb

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

def A(i, j):
    if 0.5*i <= j and j <= 2*i and (i+j)%3==0:
        n, m = (2*j-i)//3, (2*i-j)//3
        return comb(n+m,m, exact=True)%((10**9)+7)
    else:
        return 0

print(A(x, y))

Fixed submission:
x, y = map(int, input().split())

def combinations_count(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 A(i, j):
    if 0.5*i <= j and j <= 2*i and (i+j)%3==0:
        n, m = (2*j-i)//3, (2*i-j)//3
        return combinations_count(n+m,m)%((10**9)+7)
    else:
        return 0

print(A(x, y))

Buggy python submission (verdict: Time Limit Exceeded):
from operator import mul
from functools import reduce

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

def combinations_count(n, r):
    r = min(n-r,r)
    if r == 0: return 1
    over = reduce(mul, range(n, n - r, -1))
    under = reduce(mul, range(1,r + 1))
    return over // under

def A(i, j):
    if 0.5*i <= j and j <= 2*i and (i+j)%3==0:
        n, m = (2*j-i)//3, (2*i-j)//3
        return combinations_count(n+m,m)%((10**9)+7)
    else:
        return 0

print(A(x, y))

Fixed submission:
x, y = map(int, input().split())

def combinations_count(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 A(i, j):
    if 0.5*i <= j and j <= 2*i and (i+j)%3==0:
        n, m = (2*j-i)//3, (2*i-j)//3
        return combinations_count(n+m,m)%((10**9)+7)
    else:
        return 0

print(A(x, y))

Buggy python submission (verdict: Time Limit Exceeded):
from operator import mul
from functools import reduce

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

def combinations_count(n, r):
    r = min(n-r,r)
    if r == 0: return 1
    over = reduce(mul, range(n, n - r, -1))
    under = reduce(mul, range(1,r + 1))
    return over // under

def A(i, j):
    if 0.5*i <= j and j <= 2*i and (i+j)%3==0:
        n, m = (2*j-i)//3, (2*i-j)//3
        return combinations_count(n+m,m)%((10**9)+7)
    else:
        return 0

print(A(x, y))

Fixed submission:
x, y = map(int, input().split())

def combinations_count(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 A(i, j):
    if 0.5*i <= j and j <= 2*i and (i+j)%3==0:
        n, m = (2*j-i)//3, (2*i-j)//3
        return combinations_count(n+m,m)%((10**9)+7)
    else:
        return 0

print(A(x, y))

Buggy python submission (verdict: Time Limit Exceeded):
import math
x, y = map(int, input().split())

def combinations_count(n, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))

def A(i, j):
    if 0.5*i <= j and j <= 2*i and (i+j)%3==0:
        n, m = (2*j-i)//3, (2*i-j)//3
        return combinations_count(n+m,m)%((10**9)+7)
    else:
        return 0

print(A(x, y))

Fixed submission:
x, y = map(int, input().split())

def combinations_count(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 A(i, j):
    if 0.5*i <= j and j <= 2*i and (i+j)%3==0:
        n, m = (2*j-i)//3, (2*i-j)//3
        return combinations_count(n+m,m)%((10**9)+7)
    else:
        return 0

print(A(x, y))