Problem:
Score : 400 points

Problem Statement

There is a knight - the chess piece - at the origin (0, 0) of a two-dimensional grid.

When the knight is at the square (i, j), it can be moved to either (i+1,j+2) or (i+2, j+1).

In how many ways can the knight reach the square (X, Y)?

Find the number of ways modulo 10^9 + 7.

Constraints

1 \leq X \leq 10^6

1 \leq Y \leq 10^6

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X Y

Output

Print the number of ways for the knight to reach (X, Y) from (0, 0), modulo 10^9 + 7.

Sample Input 1

3 3

Sample Output 1

2

There are two ways: (0,0) \to (1,2) \to (3,3) and (0,0) \to (2,1) \to (3,3).

Sample Input 2

2 2

Sample Output 2

0

The knight cannot reach (2,2).

Sample Input 3

999999 999999

Sample Output 3

151840682

Print the number of ways modulo 10^9 + 7.

Solution in Python (3.4.3) (judge verdict: Wrong Answer)

import math

def modinv(a, m):
    b = m
    u = 1
    v = 0
    while b:
        t = a // b
        a -= t * b
        b, a = a, b
        u -= t * v
        v, u = u, v
    u = u % m
    if (u < 0):
        u += m
    return u

def fact(n):
    if n <= 1:
        return 1
    ret = 1
    for i in range(2, n + 1):
        ret *= i
        ret = ret % (10 ** 9 + 7)
    
    return ret

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

nx, ny = - x / 3 + 2 * y / 3, 2 * x / 3 - y / 3

if nx.is_integer() and ny.is_integer():
    n2x = int(nx)
    n2y = int(ny)
    gnx = modinv(fact(n2x), 10 ** 9 + 7)
    gny = modinv(fact(n2y), 10 ** 9 + 7)
    print((fact(n2x + n2y) * gnx % (10 ** 9 + 7)) * gny % (10 ** 9 + 7))
else:
    print('0')